Start with the story. Then go through each chapter, one lesson at a time. Each lesson has three short checks. Each chapter ends with a review. The unit ends with a wrap-up.
Every skater solves physics problems with their body. Standing on a narrow board, a rider keeps their center of mass over four small wheels. Leaning into a carve, they let the trucks steer and let friction pull them around a curve. Popping a 180, they twist against the ground and then ride the spin they carry into the air. Pumping a bowl, they gain speed without ever putting a foot down.
This unit names the ideas behind those moves: center of mass and base of support, the geometry of trucks, centripetal force, the limits of grip, speed wobble, torque, angular momentum and moment of inertia. You will work through real numbers in meters, seconds, kilograms and newtons, using g = 9.8 m/s². You will also learn how to set up trucks, calm a wobble, pump a bowl and practice a frontside 180 step by step, with safety first.
By the end you will be able to explain why a board turns when you lean, calculate the inward force a carve needs, predict how much faster a skater spins when they tuck, and show where the energy of a pump comes from.
When it happened
1687
Isaac Newton publishes the Principia, with his laws of motion
1729
Andrew Motte's English translation of the Principia appears
1963
Larry Stevenson's Makaha brand sells skateboards in California
1965
First National Skateboard Championships in Anaheim, California
1971
Larry Stevenson is granted a patent for the kicktail
c. 1973
Frank Nasworthy's urethane wheels give boards grip for carving
1976
Carlsbad Skatepark and Skateboard City open with curved walls to pump
c. 1978
Alan Gelfand's ollie on transition shows a board can leave the wall with the rider
1999
Tony Hawk lands a 900, two and a half spins, at the X Games
2021
Skateboarding debuts at the Tokyo 2020 Olympics with street and park events
23
Chapter
Center of Mass and Turning
Balance
Big questionHow does a skater stay on top of a narrow board and make it curve just by leaning?
The story
A Curve Drawn in Chalk Dust
A rider leans into a long carve, and the wheels leave a curve on the ground.
Late on a Saturday afternoon, Dana rolls across the empty lot behind the community center. The concrete is smooth and dry. Someone has drawn hopscotch squares in chalk near the fence, and a thin layer of chalk dust has blown across the ground.
Dana pushes twice with her back foot, then sets it on the tail. Her helmet is buckled, and her knee pads are snug. She bends her knees and lets her weight settle over her toes. The board begins to curve toward the toe side, slow and smooth, like a pencil drawing an arc.
She shifts her weight back onto her heels. The board swings the other way. Toe side, heel side, toe side again. She never steers with her hands or twists the board with her feet. She only leans, and the board answers.
When she rolls back over the chalk, she stops and looks down. Four wheels have left four thin lines in the dust. The lines are not straight. They form a long, wavy S that shows exactly where each lean began and ended.
Her friend Marcus walks over and points at the lines. "How does leaning make it turn?" he asks. "The board doesn't have a steering wheel." Dana laughs, picks up the board and flips it over to show him the trucks.
Talk about itWhen you lean on a bike, a scooter or a skateboard, what do you think makes the path curve instead of making you fall over?
Section 1
Balance and the Center of Mass
23.1
Where Your Weight Is Centered
Main ideaThe center of mass is the single point where an object's weight acts as if it were all gathered together.
Lay a ruler across one finger and slide it until it stays level. The spot where it balances is its , the point where the ruler’s weight acts as if all of it were gathered in one place. For a plain ruler, that point is right in the middle. Gravity pulls on every bit of the ruler, but you can treat all those pulls as one pull on that single point.
A standing person has a center of mass too. For most people standing straight, it sits roughly at hip level, a little below the belly button, in the middle of the body. It is not fixed to one spot on your skin. When you raise your arms, it moves up a little. When you bend your knees and crouch, it drops lower. When you lean forward, it moves forward.
A skateboard has its own center of mass, usually close to the middle of the deck between the bolts. When you stand on the board, you and the board act together. Because a rider weighs many times more than a board, the combined center of mass is mostly set by where the rider’s body is. Skaters control balance by moving their own center of mass with their knees, hips, arms and shoulders.
Words to know
center of mass
the point where an object's weight acts as if it were all gathered in one place
gravity
the pull of the Earth on every object, pulling it toward the ground
crouch
to bend the knees and hips so the body gets lower
Check yourself
1. What happens to your center of mass when you bend your knees into a crouch?
Why: Crouching brings the body closer to the ground, so the center of mass drops lower.
2. Where is the center of mass of a plain wooden ruler?
Why: A plain ruler has its weight spread evenly, so it balances in the middle.
3. Why is the combined center of mass of a rider and board set mostly by the rider?
Why: The rider is much heavier than the board, so the rider's position decides where the combined center of mass is.
23.2
The Base of Support
Main ideaAn object stays balanced while its center of mass is above its base of support.
Stand with your feet together and have a friend give your shoulder a gentle nudge. You wobble. Now stand with your feet wide apart and try again. You barely move. The difference is your , the area on the ground outlined by everything touching it. Wide feet make a wide base.
The rule of balance is simple to say. An object stays upright while a straight line down from its center of mass lands inside its base of support. If that line falls outside the base, gravity pulls the object over. A tall, narrow bookcase tips more easily than a short, wide one because a small lean moves its high center of mass past the edge of its narrow base.
A skateboard’s base of support is the rectangle between the four spots where the wheels touch the ground. From nose to tail it is long, the length of the , the distance between the front and back wheels. From toe side to heel side it is narrow, only as wide as the wheels are apart. That is why falling forward or backward off a rolling board is less common than tipping toward the toes or heels.
Words to know
base of support
the area on the ground outlined by every point that touches it, such as feet or wheels
wheelbase
the distance between the front wheels and the back wheels of a board
balance
keeping the center of mass above the base of support so you do not tip over
Check yourself
1. When does an object tip over?
Why: Gravity tips an object when the point below its center of mass is outside the base of support.
2. Which direction is a skateboard's base of support narrowest?
Why: The base is only as wide as the wheels are apart from toe side to heel side, but it is as long as the wheelbase from nose to tail.
3. What does the wheelbase measure?
Why: The wheelbase is the distance from the front wheels to the back wheels.
23.3
Staying Up on a Rolling Board
Main ideaBent knees lower the center of mass and let a rider make the small corrections that keep it over the board.
Before rolling, practice balance standing still on grass or carpet so the board cannot roll away. Wear a helmet that fits and is buckled, and add wrist guards and pads while you learn. Put your front foot just behind the front bolts and your back foot over or just in front of the back bolts. Bend your knees as if you were about to sit on a high stool, and keep your shoulders lined up over the board.
Bent knees help in two ways. First, they lower your center of mass, so a small bump moves it a shorter distance sideways. Second, they work like springs. A straight-legged rider passes every jolt from a crack straight up into the hips. A rider with soft knees can absorb the jolt and keep the upper body still. Riders make many tiny corrections to keep the center of mass over the narrow base. Each is a small shift of weight through the ankles, hips or arms.
The same idea explains a , rolling on two wheels with the nose or tail up. In a back-wheel manual, the base of support shrinks from a rectangle to a thin line between the two back wheels. The rider must hold the center of mass right over that line. Too far back and the tail scrapes; too far forward and the nose drops. Practice manuals on carpet first, with a grown-up spotter if you are young.
Words to know
correction
a small shift of weight that moves the center of mass back over the base of support
manual
rolling on only the back wheels or only the front wheels, with the other end lifted
bolts
the screws that hold the trucks to the deck; their spots on top are a guide for foot position
Check yourself
1. In a back-wheel manual, what shape does the base of support become?
Why: With only the back wheels down, the base shrinks to the line between those two wheels.
2. Where should the front foot go when you first stand on the board?
Why: The front foot goes just behind the front bolts, and the back foot goes over or just in front of the back bolts.
3. Why do bent knees help a rider stay balanced?
Why: Bent knees lower the center of mass and act like springs that soak up bumps.
Section 2
How Trucks Steer the Board
23.4
The Parts of a Truck
Main ideaA truck is a set of metal parts held together by a kingpin, with rubbery bushings that let it tilt and spring back.
Flip a skateboard over and look at one of the two , the metal assemblies that hold the wheels. The flat part screwed to the deck is the baseplate. The T-shaped part that holds the axle is the . The axle runs through the hanger and sticks out each side, and a wheel slides onto each end with two bearings inside it.
A thick bolt called the rises out of the baseplate and passes through the hanger. Around the kingpin, above and below the hanger, sit two rubbery rings called . They are usually made of urethane, the same family of material as the wheels. A nut on top of the kingpin squeezes the bushings. The bushings hold the hanger in place but let it tilt, then push it back to center.
The hanger also has a short arm, the pivot, that pokes into a small cup in the baseplate. The pivot and the kingpin together set the line the hanger swings around. That line is tilted at an angle, not flat and not straight up. Because of that slant, tilting the deck makes the hanger turn, which is the secret of steering a skateboard by leaning.
Words to know
trucks
the metal parts under the deck that hold the wheels and let the board turn
hanger
the T-shaped part of a truck that holds the axle and the wheels
kingpin
the large bolt that holds a truck together and passes through the bushings and hanger
bushings
rubbery rings around the kingpin that let the hanger tilt and then push it back to center
Check yourself
1. Which part of a truck holds the axle?
Why: The T-shaped hanger holds the axle, and the wheels go on the axle's ends.
2. What do the bushings do?
Why: The rubbery bushings allow the hanger to tilt, then spring it back to the middle.
3. What passes through the bushings and the hanger?
Why: The kingpin is the large bolt that rises from the baseplate through the bushings and hanger.
23.5
Leaning Turns the Wheels
Main ideaBecause the hanger swings on a slanted line, tilting the deck turns the axles, and the board curves toward the side you lean.
Stand on a board on carpet and press down with your toes. The deck tilts toward the toe side. Underneath, each hanger swings on its slanted pivot line. A swing on a slanted line does two things at once: it lets the deck tilt, and it twists the axle so it no longer points straight across. The wheels now point a little to one side, the way the front wheels of a car point when the steering wheel is turned.
The front and back trucks face opposite ways, with their kingpins pointing toward each other. So when the deck tilts, the front axle and the back axle twist in opposite directions. Seen from above, the two axles are no longer parallel. Lines drawn out along the two axles would meet at a point off to one side of the board. That point is the center of the circle the board will roll around.
The result is easy to remember. Lean toward your toes and the board turns toward your toe side. Lean toward your heels and it turns toward your heel side. The harder you lean, the more the axles twist and the tighter the circle. This is called when you ride long, smooth arcs by leaning instead of lifting the front wheels. The is the radius of the circle the board traces.
Words to know
carving
riding long, smooth curves by leaning the board instead of lifting it
turning radius
the radius of the circle a board traces as it turns; smaller means a tighter turn
axle
the metal rod through the hanger that the wheels spin on
Check yourself
1. A rider presses down with the toes. Which way does the board turn?
Why: Leaning toward the toes tilts the deck and twists the axles so the board curves toward the toe side.
2. Why do the front and back axles twist in opposite directions when the deck tilts?
Why: The two trucks are mounted facing each other, so the same tilt swings their axles opposite ways.
3. What happens to the turning radius when a rider leans harder?
Why: A harder lean twists the axles more, so the circle gets smaller and the turn is tighter.
23.6
Tight Trucks and Loose Trucks
Main ideaTightening the kingpin nut or using harder bushings makes a board steadier but slower to turn; loosening does the opposite.
Turning the kingpin nut with a skate tool changes how the board rides. Turning it clockwise squeezes the bushings, so the board has : the hanger needs more lean to tilt, and the board resists turning. Turning it counterclockwise lets the bushings relax, so the board has : a small lean makes a sharp turn.
Each choice has a cost. Tight trucks feel steady at speed and are less likely to shake, but they make sharp turns harder. Loose trucks carve tight circles and feel lively, but they react to every small wobble of the rider’s ankles. Many riders adjust a quarter turn at a time, ride for a while, and adjust again. Bushings also come in different hardness, measured on a durometer scale like wheels. Softer bushings turn easier; harder ones feel steadier.
Keep the nut threaded far enough onto the kingpin that its locking ring grips the threads. A nut backed off too far can loosen on its own while you ride. Check both trucks after adjusting one, since uneven trucks make the board pull to one side. If the board turns too sharply while you are still learning to roll, tighten the trucks a little before you change anything else.
Words to know
tight trucks
trucks with the kingpin nut turned down so the bushings are squeezed; steadier, slower to turn
loose trucks
trucks with the bushings less squeezed; quick, sharp turning but less steady
durometer
a scale that measures how hard a rubbery material is, used for wheels and bushings
Check yourself
1. What happens when you turn the kingpin nut clockwise?
Why: Turning the nut clockwise squeezes the bushings, which makes the trucks tighter.
2. Which is a trade-off of loose trucks?
Why: Loose trucks turn easily but are less steady because small weight shifts steer the board.
3. Why should the kingpin nut stay far enough down on the threads?
Why: The nut's locking ring has to grip the threads, or the nut can work loose during a ride.
Section 3
The Physics of a Turn
23.7
Why a Turn Needs a Force
Main ideaA moving object goes straight unless a force pushes it sideways; in a turn, friction from the ground pushes the board toward the center of the curve.
Roll a marble across a smooth floor and it keeps going in a straight line until something stops it or pushes it aside. This is , the tendency of a moving object to keep moving at the same speed in the same direction. Isaac Newton put it at the center of his first law of motion in 1687. A skater rolling across flat concrete would also go straight forever if no force acted.
To travel in a curve, an object needs a force that keeps pulling it toward the inside of the curve. This inward force is called , which means center-seeking. Swing a ball on a string in a circle and the string is that force: it pulls the ball toward your hand. Let go of the string and the ball flies off in a straight line, not outward in a curve.
On a skateboard, nothing pulls on a string. The inward force comes from between the wheels and the ground. When the axles twist, the wheels try to roll in a curve, and the ground grips the urethane and pushes the wheels sideways toward the center of the circle. Even at a steady speed, a turning board keeps changing its direction of motion, so physicists say it is accelerating.
Words to know
inertia
the tendency of an object to keep doing what it is doing: staying still, or moving straight at the same speed
centripetal force
the inward force that keeps an object moving in a curve, pointing toward the center of the circle
friction
a force between two surfaces that resists sliding; it lets wheels grip the ground
Check yourself
1. On a turning skateboard, what supplies the centripetal force?
Why: The ground grips the wheels and pushes them sideways toward the center of the curve.
2. What does centripetal mean?
Why: Centripetal means center-seeking; the force points toward the center of the circle.
3. You swing a ball on a string and let go. Which way does the ball go?
Why: With no inward pull, inertia carries the ball in a straight line.
23.8
Leaning Into the Carve
Main ideaIn a turn the rider leans toward the center so the ground's push stays in line with the center of mass; faster or tighter turns need more lean.
Watch a rider carve and you will see the whole body tilt toward the inside of the turn. This lean is not just style. The ground pushes up on the wheels and also sideways, toward the center of the turn. If the rider stood straight up, that sideways push at the feet would tip them toward the outside, the way a rug pulled from under your feet tips you over. Leaning lines up the ground’s total push with the rider’s center of mass.
The needed inward depends on speed and radius: a = v² ÷ r, where v is speed in meters per second and r is the turning radius in meters. Worked example: a rider rolls at 5 m/s around a curve with a 5 m radius. Then a = 5² ÷ 5 = 25 ÷ 5 = 5 m/s². If the rider and board together have a of 60 kg, the inward force is F = ma = 60 × 5 = 300 N.
Compare that with the rider’s weight: W = mg = 60 × 9.8 = 588 N. The sideways force is about half the weight, since 300 ÷ 588 ≈ 0.51. A rider leaning at about 27 degrees from straight up keeps the push balanced in this turn. The lean depends only on speed and radius, not on mass, so a light rider and a heavy rider carving the same line at the same speed lean the same amount.
Words to know
acceleration
a change in speed or direction each second, measured in meters per second squared (m/s²)
mass
how much matter an object has, measured in kilograms
newton
the unit of force; one newton gives a 1 kg mass an acceleration of 1 m/s²
Check yourself
1. A rider goes 4 m/s around a curve with a 2 m radius. What is the inward acceleration?
Why: a = v² ÷ r = 4² ÷ 2 = 16 ÷ 2 = 8 m/s².
2. Why does a rider lean toward the inside of a turn?
Why: Leaning keeps the ground's combined push in line with the center of mass so the rider does not tip outward.
3. What is the weight of a 60 kg rider?
Why: Weight is W = mg = 60 × 9.8 = 588 N.
23.9
Speed, Radius and Grip
Main ideaFriction can only push so hard; if a turn needs more inward force than the wheels can grip, the board slides.
The formula a = v² ÷ r has a surprise inside it. Because speed is squared, doubling the speed makes the needed inward force four times as large. Going three times faster needs nine times the force. Cutting the radius in half doubles the force. A turn that feels easy at a slow roll can be impossible at a fast one.
Friction has a limit. The most sideways grip the wheels can give is roughly μ × N, where N is the pressing the wheels into the ground and μ (the Greek letter mu) is the , a number that describes how grippy two surfaces are together. On level ground N equals the weight, so the largest possible turning acceleration is about μ × g. For example, if μ were about 0.7, the limit would be about 0.7 × 9.8 ≈ 6.9 m/s².
In that example, a rider at 8 m/s on a 5 m radius would need 8² ÷ 5 = 64 ÷ 5 = 12.8 m/s², almost twice the limit, so the wheels would slip. Skaters who want that slide do it on purpose in a powerslide, turning the board sideways to scrub off speed. Softer wheels usually grip rough ground better, and hard wheels slide more easily on smooth concrete. Sand, water and leaves lower μ a lot, which is why a wet or dusty turn can send a board out from under a rider.
Words to know
normal force
the push of a surface straight out against whatever presses on it; on level ground it equals the weight
coefficient of friction
a number, written μ, that describes how strongly two surfaces grip; bigger means more grip
powerslide
turning the board sideways on purpose so the wheels slide and the rider slows down
Check yourself
1. If a rider doubles her speed through the same curve, the needed inward force becomes:
Why: Speed is squared in a = v² ÷ r, so twice the speed needs 2² = 4 times the force.
2. On level ground, what is the largest possible turning acceleration before the wheels slide?
Why: The grip limit is μN, and on level ground N = mg, so the limit on acceleration is μg.
3. Why can a sandy patch make a board slide out in a turn?
Why: Sand lowers μ, so the wheels cannot give as much sideways grip as the turn needs.
Section 4
Speed Wobble
23.10
What Speed Wobble Is
Main ideaSpeed wobble is a fast side-to-side shaking that feeds on itself, most often at higher speeds with loose trucks or stiff legs.
A rider is rolling faster than usual down a gentle slope in an empty lot. The board starts to shimmy: the trucks twitch left and right, a little at first, then harder and faster. Riders call this . It can grow in a second or two from a buzz in the feet to a shake strong enough to throw the rider off.
Speed wobble is an , a motion that swings back and forth over and over. On a skateboard it can feed on itself. A tiny tilt steers the trucks, the turn tips the rider the other way, the rider corrects, and the correction overshoots into a tilt the other way. At higher speeds each swing happens faster than the rider can react smoothly, so the corrections arrive late and make the next swing bigger.
Several things make wobble more likely. Loose trucks or soft bushings let a small lean turn the wheels a lot. Stiff, straight legs pass every twitch through the body instead of soaking it up. Weight drifting onto the back foot is a common trigger, because it lets the front of the board wander. Going faster than you have practiced is the biggest factor of all. Wobble is not a sign that someone is a poor skater; experienced riders feel it too.
Words to know
speed wobble
a fast side-to-side shaking of the board and trucks that tends to grow at higher speeds
oscillation
a motion that swings back and forth over and over, like a swing or a plucked string
overcorrect
to push too far when fixing a lean, so you tip the other way
Check yourself
1. What is an oscillation?
Why: An oscillation is a repeating back-and-forth motion, like a swing.
2. Which setup makes speed wobble more likely?
Why: Loose trucks let small leans steer a lot, and stiff legs pass every twitch through the body.
3. Why does wobble grow at higher speeds?
Why: At speed the swings come quickly, so late corrections overshoot and make the next swing bigger.
23.11
Calming a Wobble
Main ideaTo calm speed wobble, crouch lower, press gently on the front foot, relax and look ahead; prevent it by riding within your skill and setting trucks a little tighter.
When the board starts to shake, the first move is to get low. Bend your knees and drop your hips so your center of mass sits closer to the board. A lower body swings less, and bent legs soak up the twitching. Next, move your weight forward so you press gently on your front foot. Pressure on the front truck helps hold it steady and keeps the front of the board from wandering. Then relax your ankles and look far ahead, not down at your feet.
Fighting the board with sharp, quick corrections usually makes wobble worse, because each sudden push becomes the next swing. Smooth, small pressure works better. If the shaking keeps growing and you are moving slowly enough, step off and run it out. If not, bail low: crouch, aim for the grass if it is close, and fall onto your pads and roll instead of reaching out with straight, locked arms.
Prevention is the best fix. Learn speed a little at a time on flat ground and gentle, empty slopes. Never ride hills that have cars, and never hold onto a moving vehicle. Tighten loose trucks a quarter turn, or try harder bushings, before riding faster. Wear a helmet that fits and is buckled, plus wrist guards and pads, every time you practice speed. Fear when the board shakes is a normal, useful signal that it is time to slow down.
Words to know
stance
how a rider stands on the board: where the feet go and how low the body is
bail
to leave the board on purpose to avoid a worse fall
front foot
the foot nearer the nose of the board; for regular riders it is the left, for goofy riders the right
Check yourself
1. When speed wobble starts, which foot should you press gently with?
Why: Gentle pressure on the front foot helps hold the front truck steady.
2. Why do sharp, quick corrections usually make wobble worse?
Why: Sudden pushes overshoot and feed the back-and-forth motion.
3. Which change helps prevent speed wobble?
Why: Slightly tighter trucks and gradual speed practice make wobble less likely.
Chapter review
Center of Mass and Turning
0 / 8
1. A skater stays balanced as long as the line down from the center of mass falls:
Why: Balance means the center of mass stays above the base of support.
2. Which part of the truck is squeezed when you tighten the kingpin nut?
Why: The kingpin nut presses on the bushings; squeezing them makes the trucks tighter.
3. A rider leans toward the heels. What does the board do?
Why: Leaning tilts the deck, the axles twist, and the board curves toward the side of the lean.
4. A 50 kg rider turns at 4 m/s on a 4 m radius. What inward force is needed?
Why: a = 4² ÷ 4 = 16 ÷ 4 = 4 m/s², and F = ma = 50 × 4 = 200 N.
5. What is inertia?
Why: Inertia is an object's tendency to keep doing what it is doing unless a force acts.
6. Why does the board slide out in a turn that is too fast or too tight?
Why: Friction has a limit of about μN; a turn that needs more than that makes the wheels slip.
7. Which stance helps calm a speed wobble?
Why: A low stance with weight on the front foot steadies the board.
8. Why is a skateboard easier to tip toward the toes or heels than forward or backward?
Why: The wheels are close together side to side but far apart nose to tail, so the side-to-side base is narrow.
Send it to your teacher
24
Chapter
Rotation and Angular Momentum
Rotation
Big questionOnce a skater leaves the ground, what decides how fast and how far they can spin?
The story
The Spinning Stool
A skater on a lab stool pulls in her arms and spins faster without anyone pushing.
The physics room smells like dry-erase markers. In the middle of the floor sits a round lab stool that turns freely on its base. Ms. Ortiz holds up two plastic water bottles, each filled to the top. "Who wants to spin?" she asks. Jaylen, who skates the park after school every day, raises his hand first.
He sits on the stool and holds a bottle in each hand with his arms stretched straight out to the sides. Ms. Ortiz gives the stool a gentle push and steps back. Jaylen turns slowly, like a ceiling fan on its lowest setting. The class counts the turns out loud.
"Now pull them in," she says. Jaylen bends his elbows and hugs the bottles to his chest. The stool whips around so fast the class gasps. Nobody touched him. He pushes his arms back out, and the stool slows down again, as if someone had stepped on a brake.
Jaylen plants his feet to stop and laughs. "That's what happens on a 360," he says. "If I keep my arms out, I can't get all the way around. If I tuck them, the board comes around on its own." Ms. Ortiz writes two words on the board: angular momentum.
Talk about itNobody pushed Jaylen a second time. Where do you think the extra speed came from when he pulled his arms in?
Section 1
Spin and Torque
24.1
Spinning Things Keep Spinning
Main ideaAngular momentum, the amount of spin an object carries, stays the same unless an outside torque changes it.
Spin a top on a smooth table and it keeps turning for a long time. It slows only because the table rubs its point and the air drags on it. Just as a rolling object tends to keep rolling straight, a spinning object tends to keep spinning. Physicists measure the amount of spin an object carries as its .
Angular momentum depends on two things. One is how fast the object turns, called its , often counted in rotations per second. The other is how its mass is spread out around the line it spins on, the . Written as a formula, L = Iω, where L is angular momentum, I is the moment of inertia (the spread of mass) and ω, the Greek letter omega, is the angular velocity.
The key rule is : if no outside twist acts on an object, its angular momentum stays exactly the same. A skater in the air is a clear case. The air pushes back only a little, and nothing else can twist the skater, so the spin they carry when their wheels leave the ground is the spin they have until they land. They can change how it is shared out, but not the total.
Words to know
angular momentum
the amount of spin an object carries; it equals moment of inertia times angular velocity (L = Iω)
angular velocity
how fast something turns, such as rotations per second
axis of rotation
the imaginary line an object spins around
conservation of angular momentum
the rule that total angular momentum stays the same unless an outside torque acts
Check yourself
1. In the formula L = Iω, what does ω stand for?
Why: ω (omega) is the angular velocity, how fast the object turns.
2. When does an object's angular momentum stay the same?
Why: Conservation of angular momentum holds when no outside twist acts.
3. What is the axis of rotation?
Why: The axis of rotation is the line the object turns around.
24.2
Torque Starts and Stops a Spin
Main ideaA torque is a twist; it equals the force times the lever arm, and it is the only thing that changes angular momentum.
Push on a door near its handle and it swings open easily. Push with the same force right next to the hinges and it barely moves. The difference is , the twisting effect of a force. Torque equals the force times the , the distance from the pivot to where the force is applied, measured straight across. The unit is the newton-meter (N·m).
Worked example: you push on a door with a force of 20 N. At the handle, 0.8 m from the hinges, the torque is 20 × 0.8 = 16 N·m. Near the hinges, 0.1 m away, the torque is 20 × 0.1 = 2 N·m. The same push gives eight times the twist at the handle, because 16 ÷ 2 = 8. A longer lever arm means more turning effect from the same force.
A skateboard is full of lever arms. In a kickturn, the back foot presses on the tail, and the back wheels are the pivot. The tail sticks out past the back wheels, so a press on its end has a lever arm that lifts the nose. To spin the whole body, a skater needs torque from the ground through their feet. Friction between the shoes, the grip tape and the wheels on the ground lets the feet twist the board and body before takeoff.
Words to know
torque
the twisting effect of a force; torque equals force times lever arm
lever arm
the distance from a pivot to the line where a force pushes
pivot
the point or line something turns around
newton-meter
the unit of torque: one newton of force on a one-meter lever arm
Check yourself
1. A skater presses with 300 N on the tail, 0.15 m behind the back axle. What is the torque about the axle?
Why: Torque = force × lever arm = 300 × 0.15 = 45 N·m.
2. Why does a door open more easily when you push at the handle?
Why: The handle is far from the hinges, so the same force makes a larger torque.
3. Where does a skater get the torque to start a spin?
Why: Twisting against the ground through the feet supplies the torque; the air cannot.
24.3
Winding Up for a 180
Main ideaSkaters wind their shoulders the opposite way, then unwind as they pop, so the ground gives them spin before they leave it.
Watch a skater set up a 180 and you will see a small move before the pop. Their shoulders and arms turn a little the opposite way, like a baseball batter pulling the bat back. This is the . A skater about to spin toward the front, for example, first turns the shoulders slightly toward the back.
The wind-up gives the skater a longer time and a bigger turn to work with. As they crouch and pop, they swing the shoulders hard in the spin direction. Their feet are still pressing on the board, and the wheels are still on the ground, so the twist of the upper body pushes against the ground through the legs. The ground pushes back with friction, and that outside torque gives the whole skater angular momentum just before takeoff.
Once the skater is in the air, the wind-up rule changes. Now the total spin is fixed. If the shoulders keep turning one way, the hips and legs swing slightly the other way to balance it. That is why skaters lead with the shoulders, let the hips follow, and let the board follow the hips. This , twisting the upper body one way so the lower body turns the other, is how a skater lines up the board in the air without changing the total spin.
Words to know
wind-up
turning the shoulders and arms a little the opposite way before spinning
counter-rotation
twisting one part of the body one way so another part turns the opposite way
pop
the snap of the tail against the ground that sends the board up in an ollie
Check yourself
1. Why must the shoulders swing while the wheels are still on the ground?
Why: The ground's friction provides the torque only while the skater is still touching it.
2. In the air, the shoulders keep turning one way. What do the hips and legs do?
Why: Total spin is fixed in the air, so turning the upper body one way swings the lower body the other way.
3. In what order do the body and board turn in a 180?
Why: Skaters lead with the shoulders, the hips follow, and the board follows the hips.
Section 2
Arms In, Spin Faster
24.4
The Stool Experiment
Main ideaPulling the arms in lowers the moment of inertia, so the spin speeds up to keep angular momentum the same.
Jaylen’s stool spin is a classic physics demonstration. With his arms out, his mass is spread far from the axis of rotation. With his arms in, more of his mass sits close to the axis. Nothing outside twists him either way. Since his angular momentum L = Iω cannot change, a smaller I has to go with a larger ω.
Worked example with made-up but realistic numbers: suppose Jaylen and the stool have a moment of inertia of 3.0 kg·m² with his arms out, and he turns at 1 rotation per second. His angular momentum is 3.0 × 1 = 3.0 units. He pulls in, and his moment of inertia drops to 1.5 kg·m². Then 1.5 × ω = 3.0, so ω = 3.0 ÷ 1.5 = 2 rotations per second. Halving I doubles the spin rate.
Skaters use this every time they spin. In a 360 on a ramp or a big spin in the air, a skater who tucks the arms close and keeps the knees bent turns faster with the same takeoff. Reaching the arms out works the other way: it slows the spin. That is useful near the landing. Skaters often the landing, turning the head to look at it, and open the arms a little to slow down and settle before the wheels touch.
Words to know
moment of inertia
how hard it is to change an object's spin; it is larger when mass is spread far from the axis
rotation
one full turn of 360 degrees around an axis
spot
to look at the landing during a spin so you know where you will come down
Check yourself
1. A skater's moment of inertia drops from 2.4 to 1.2 kg·m² in the air. If they started at 1 rotation per second, how fast do they spin now?
Why: L stays 2.4 × 1 = 2.4, so ω = 2.4 ÷ 1.2 = 2 rotations per second.
2. Why does pulling the arms in make a skater spin faster?
Why: With L fixed, a smaller I means a larger ω.
3. Why might a skater open the arms a little near the landing?
Why: Spreading the arms raises the moment of inertia, which slows the spin.
24.5
How Mass Spread Out Matters
Main ideaMoment of inertia grows with the square of distance from the axis, so mass far out counts much more than mass close in.
For a small heavy object turning around an axis, the moment of inertia is I = m × r², where m is the mass in kilograms and r is the distance from the axis in meters. The unit is kilogram meter squared (kg·m²). The square matters a great deal. Moving a weight twice as far out makes its moment of inertia four times as large.
Worked example: hold a 2 kg dumbbell 0.2 m from your body’s axis. Its moment of inertia is 2 × 0.2² = 2 × 0.04 = 0.08 kg·m². Stretch your arm so it is 0.8 m out. Now I = 2 × 0.8² = 2 × 0.64 = 1.28 kg·m². Moving it four times as far out made it sixteen times harder to spin, because 1.28 ÷ 0.08 = 16. A whole body is many small pieces added up the same way.
This explains how skaters shape their spins. In a tight tuck, arms, knees and head stay close to the axis, so the moment of inertia is small and the body turns quickly. A skater stretched out straight, arms wide, has a large moment of inertia and turns slowly. The board counts too. A deck held flat under the feet near the axis adds little, but a board flung out to the side adds a lot.
Words to know
kilogram meter squared
the unit of moment of inertia, written kg·m²
tuck
a body position with knees and arms pulled in close to the middle
square
a number multiplied by itself, such as 0.8 × 0.8 = 0.64
Check yourself
1. What is the moment of inertia of a 3 kg weight held 0.5 m from the axis?
Why: I = m × r² = 3 × 0.5² = 3 × 0.25 = 0.75 kg·m².
2. A weight is moved twice as far from the axis. Its moment of inertia becomes:
Why: I depends on r², and 2² = 4.
3. Which body position has the smallest moment of inertia?
Why: A tuck keeps the body's mass close to the axis, so I is smallest.
24.6
Where the Extra Spin Energy Comes From
Main ideaA faster spin has more motion energy, and that energy comes from the muscles doing work to pull the arms in.
If angular momentum stays the same, where does the extra speed come from? The answer is , the motion energy of a spin. It equals ½ × I × ω², with ω measured in radians per second. A is a way of measuring angle; one full rotation is 2π radians, about 6.28 radians.
Worked example using the stool numbers: 1 rotation per second is about 6.28 radians per second. With the arms out, the energy is ½ × 3.0 × 6.28² = 1.5 × 39.4 ≈ 59 J. With the arms in, the spin is 2 rotations per second, about 12.57 radians per second. Now the energy is ½ × 1.5 × 12.57² = 0.75 × 158 ≈ 118 J. The spin energy doubled, from about 59 J to about 118 J.
The extra energy came from Jaylen’s arms. Pulling heavy bottles inward while spinning takes effort, because the bottles tend to fly outward in a straight line. His muscles did , which is force applied over a distance, and that work became spin energy. When he reached back out, the energy went the other way. A skater who tucks hard in the air is doing the same work with arms, legs and core.
Words to know
rotational kinetic energy
the motion energy of a spinning object, equal to ½ × I × ω²
radian
a unit of angle; one full turn is 2π radians, about 6.28
work
energy moved by a force pushing or pulling something over a distance; measured in joules
Check yourself
1. About how many radians are in one full rotation?
Why: One rotation is 2π radians, about 6.28.
2. When the stool rider pulls the arms in, what happens to the rotational kinetic energy in the example?
Why: With I halved and ω doubled, ½Iω² goes from about 59 J to about 118 J.
3. Where does the extra spin energy come from?
Why: The muscles do work pulling the weights inward, and that work becomes spin energy.
Section 3
Pumping a Bowl
24.7
How to Pump
Main ideaTo pump, crouch as you ride into each curve of the bowl, then push up to stand tall as you pass through the curve.
A is a skatepark pool with curved walls all around. A rider can gain speed in it without ever pushing with a foot. The trick is : crouching and standing at the right moments. Before you try, you should already roll comfortably on flat ground and ride up and down a small , the curved part where a wall meets the floor. Wear a helmet that is buckled, plus knee pads, elbow pads and wrist guards, and start in a small, shallow bowl when it is not crowded.
First, roll across the bottom with your knees bent and your weight centered between the bolts. Next, as you ride down a wall toward the curve, sink low into a crouch. Then, as the board passes through the curve and you feel your feet pressed harder into the deck, push up through both legs and stand tall, like a jump that never leaves the board. Ride up the next wall a little, crouch again as you come back down, and push again through the curve.
It feels like a rhythm: low, push, low, push. Common problems have simple fixes. If you push too early, on the flat, you gain almost nothing, so wait until you feel the curve press into your feet. If you lean back on the way up a wall, your board can shoot out in front of you; keep your shoulders over your feet. If you do fall, try to land on your knee pads and slide down the wall instead of putting out straight arms.
Words to know
bowl
a skatepark pool with curved walls on every side
pumping
crouching and then standing up at the right moments to gain speed on curved walls without pushing
transition
the curved part of a ramp or bowl where the floor bends up into the wall
Check yourself
1. When should a rider push up and stand tall while pumping?
Why: The push works best in the curve, where the deck presses hardest into the feet.
2. What is a transition?
Why: A transition is the curve between the floor and the wall.
3. What is a safe way to fall in a bowl?
Why: Sliding on knee pads spreads the fall out; locked arms can hurt the wrists.
24.8
Why Pumping Adds Speed
Main ideaStanding up where the curve pushes hardest lets the legs do more work than crouching gives back, and the extra becomes speed.
In a curve, the deck must push the rider toward the center of the curve, not just hold them up. So the push on the feet is larger than the rider’s weight. Worked example: a 60 kg rider moves at 5 m/s through a curve with a 2 m radius. The extra inward acceleration is v² ÷ r = 25 ÷ 2 = 12.5 m/s². At the bottom of the curve the deck pushes with about 60 × (9.8 + 12.5) = 60 × 22.3 ≈ 1,338 N. On the flat it pushes only 60 × 9.8 = 588 N.
Standing up means pushing against that force over a distance, and work equals force times distance. Raising the body 0.3 m in the curve takes about 1,338 × 0.3 ≈ 401 J of work. Crouching again on a wall or the flat, where the push is near 588 N, gives back only about 588 × 0.3 ≈ 176 J. The difference, about 401 − 176 = 225 J, stays in the motion as extra .
Check the gain: at 5 m/s the rider’s kinetic energy is ½ × 60 × 5² = 750 J. Adding 225 J gives 975 J, so the new speed is √(2 × 975 ÷ 60) = √32.5 ≈ 5.7 m/s. Angular momentum gives a second view of the same idea. In the curve, the rider circles around the curve’s center, and standing up moves their mass closer to that center, like Jaylen pulling his arms in. A child on a playground swing pumps in a similar way.
Words to know
kinetic energy
the energy of motion, equal to ½ × mass × speed²
joule
the unit of energy and work; one newton pushing over one meter is one joule
apparent weight
how heavy you feel, which is the push of the surface under you; it grows in a curve
Check yourself
1. Why is the push on a rider's feet bigger in the curve than on the flat?
Why: In a curve the deck supplies the inward centripetal push on top of holding up the rider's weight.
2. In the example, about how much energy does one pump add?
Why: Standing in the curve takes about 401 J, crouching gives back about 176 J, and 401 − 176 ≈ 225 J.
3. What is the kinetic energy of a 60 kg rider at 4 m/s?
Why: KE = ½ × 60 × 4² = 30 × 16 = 480 J.
Section 4
Frontside and Backside
24.9
What Frontside and Backside Mean
Main ideaFrontside means your chest and toes face the wall or the direction of a spin; backside means your back and heels face it.
Skaters describe direction by which side of the body faces something, not by left or right. When you ride up to a wall or a ledge with your chest and toes facing it, you are riding . When your back and heels face it, you are riding . This works the same for regular riders, who stand with the left foot forward, and goofy riders, who stand with the right foot forward.
Spins use the same idea. In a frontside spin, the skater turns so the chest swings around toward the direction of travel, and during a frontside 180 the skater faces forward halfway through. In a backside spin, the back turns toward the direction of travel first, so halfway through a backside 180 the skater’s back faces where they are headed. Because the words describe the body, a regular and a goofy rider doing a frontside 180 actually turn in opposite directions as seen from above.
These words also name grinds, slides and airs. A frontside grind on a curb means you approach with the curb on your toe side. A backside grind means the curb is on your heel side. After a 180, the skater rolls : in their normal stance, but moving backward with the tail in front. Learning both directions balances the body and gives a skater more ways to ride a park.
Words to know
frontside
facing the wall, obstacle or direction of a spin with your chest and toes
backside
facing the wall, obstacle or direction of a spin with your back and heels
fakie
riding in your normal stance but rolling backward, tail first
goofy
a stance with the right foot forward; regular is the left foot forward; both are normal
Check yourself
1. A skater rolls toward a ledge with the ledge on the heel side. How is the skater riding?
Why: Backside means the back and heels face the obstacle.
2. What does riding fakie mean?
Why: Fakie is your normal stance, moving tail first.
3. Halfway through a frontside 180, which way is the skater facing?
Why: In a frontside spin, the chest swings toward the direction of travel.
24.10
The Frontside 180 Ollie
Main ideaA frontside 180 ollie is an ollie with a wind-up: shoulders turn first, the hips follow, and the board lands rolling fakie.
Learn this only after your ollie is steady and you can roll fakie comfortably. Practice on smooth, flat, empty ground in a helmet and pads. A good first step is the frontside kickturn 180: while rolling slowly, press the tail, lift the front wheels, and pivot all the way around on the back wheels, turning your chest toward the direction you are going. This teaches the shoulder-first turn with the wheels still near the ground.
For the ollie version, set your feet as for an ollie: the ball of your back foot on the tail and your front foot just behind the front bolts. First, crouch and wind your shoulders slightly backside. Next, pop the tail with your back foot and, at the same moment, swing your shoulders frontside and slide your front foot up toward the nose. Then let your hips follow your shoulders and guide the board around with both feet. Finally, land with both feet over the bolts, knees bent, rolling fakie.
Two problems are common. If the board turns only about 90 degrees, your shoulders probably stopped early; wind up a little more and turn your head to spot the landing over your front shoulder. If you land with one foot off the board, your front foot may have dragged too far; level the board by pressing evenly with both feet in the air. Start with a small pop. Height can come later, once the turn feels smooth.
Words to know
kickturn
pressing the tail to lift the front wheels and pivoting on the back wheels
ollie
a jump where the back foot pops the tail and the front foot slides up to level the board in the air
back foot
the foot nearer the tail of the board
Check yourself
1. What should a skater practice before the frontside 180 ollie?
Why: The frontside kickturn 180 teaches the shoulder-first turn with the wheels near the ground.
2. In a frontside 180 ollie, which foot pops the tail?
Why: The back foot pops the tail while the front foot slides up toward the nose.
3. The board turns only about 90 degrees. What is the likely fix?
Why: A short turn usually means the shoulders stopped early; more wind-up and turning the head helps.
24.11
Practicing Spins Safely
Main ideaSpins are learned in small steps: quarter turns, then half turns, low and slow, with a plan for falling.
Every big spin is built from small ones. Many skaters start with tic-tac style quarter turns, lifting the front wheels and pivoting about 90 degrees on the back wheels while standing still on carpet. Next they try a full 180 kickturn standing still, then rolling slowly. Only after that do they add a small pop. Each step should feel calm before the next one begins. Fear is a normal signal that a step is too big; break it into a smaller piece.
Spinning in both directions matters. Most skaters find one direction easier at first. Practicing backside 180s as well as frontside 180s balances the body and teaches the brain to spot the landing from both shoulders. A backside 180 uses the same physics: wind the shoulders frontside, pop, then swing the shoulders backside so your back turns toward the direction of travel.
Falling small is part of every spin practice. If a landing goes wrong, step off the board toward the side it is not rolling, bend your knees, and let your body crouch. If you are going down, aim to land on pads and roll onto the side of your body, keeping your arms bent rather than locked straight. Wrist injuries are among the most common skateboarding injuries, and wrist guards help prevent them, which is why they belong on every spin session.
Words to know
progression
learning a skill in small steps, each a little harder than the last
backside 180
a half turn in which the skater's back turns toward the direction of travel first
wrist guards
pads with stiff splints that protect the wrists in a fall
Check yourself
1. What is the best first step toward learning a 180 spin?
Why: Progression starts with small pivots while standing still before adding rolling and pop.
2. In a backside 180, which way do the shoulders swing after the pop?
Why: The skater winds frontside first, then swings the shoulders backside after the pop.
3. Why do wrist guards belong on every spin session?
Why: Wrist injuries are common in skateboard falls, and wrist guards help prevent them.
Chapter review
Rotation and Angular Momentum
0 / 8
1. What does angular momentum depend on?
Why: L = Iω, the moment of inertia times the angular velocity.
2. A 25 N push is applied 0.4 m from a pivot. What is the torque?
Why: Torque = force × lever arm = 25 × 0.4 = 10 N·m.
3. Why do skaters wind up their shoulders before a 180?
Why: Swinging the shoulders while the feet press the board lets the ground provide the torque for the spin.
4. A skater in the air pulls in arms and knees. What happens?
Why: A smaller moment of inertia with the same angular momentum means a faster spin.
5. Moment of inertia is larger when:
Why: I = m × r², so mass farther from the axis counts much more.
6. While pumping a bowl, when does the rider crouch?
Why: The rider sinks low coming down the wall, then stands tall through the curve.
7. A goofy rider's chest and toes face a ledge. How is the rider riding?
Why: Frontside means chest and toes face the obstacle, for goofy and regular riders alike.
8. After a frontside 180 ollie, the skater rolls away:
Why: A 180 reverses the board, so the skater rolls backward in their normal stance, which is fakie.
Send it to your teacher
★
Unit wrap-up
Balance, Turning and Spin
Twelve words, twelve meanings
0 / 12
Tap a word, then tap its meaning. A right pair locks in green.
Words
Meanings
Unit test
Fifteen questions across the unit
0 / 15
1. A skater tips over when the line down from the center of mass:
Why: Gravity tips an object once its center of mass is no longer above its base of support.
2. What makes a skateboard turn when the rider leans?
Why: Truck geometry turns a tilt of the deck into a twist of the axles, which steers the board.
3. Turning the kingpin nut counterclockwise makes the trucks:
Why: Loosening the nut lets the bushings relax, so a smaller lean turns the board.
4. A 70 kg rider carves at 3 m/s on a 3 m radius. What inward force is needed?
Why: a = 3² ÷ 3 = 9 ÷ 3 = 3 m/s², and F = ma = 70 × 3 = 210 N.
5. What supplies the centripetal force on a carving skateboard?
Why: The ground grips the wheels and pushes them toward the center of the turn.
6. If the coefficient of friction were about 0.5, what is the largest turning acceleration on level ground?
Why: The grip limit is μg = 0.5 × 9.8 = 4.9 m/s².
7. During speed wobble, a helpful move is to:
Why: A low stance with gentle front-foot pressure calms the wobble; sharp corrections and back-foot weight feed it.
8. What is torque?
Why: Torque equals force times the lever arm and is what changes a spin.
9. Why can't a skater start spinning once they are in the air?
Why: With no ground to push on, nothing outside can twist the skater, so angular momentum stays fixed.
10. A spinning skater's moment of inertia drops from 4.0 to 2.0 kg·m². The spin rate:
Why: L = Iω stays fixed, so halving I doubles ω.
11. What is the moment of inertia of a 4 kg weight held 0.5 m from the axis?
Why: I = m × r² = 4 × 0.5² = 4 × 0.25 = 1 kg·m².
12. Where does the extra energy of a faster spin come from when a skater tucks?
Why: Pulling the arms and legs inward takes work, and that work becomes spin energy.
13. Why does standing tall in the curve of a bowl add speed?
Why: The deck pushes harder in the curve, so standing there does more work than crouching later returns; the extra becomes kinetic energy.
14. A regular rider rolls toward a curb with the curb on the heel side. The rider is riding:
Why: Backside means the back and heels face the obstacle.
15. In a frontside 180 ollie, what is the order of the turn?
Why: The shoulders lead, the hips follow, and the board follows the hips.
Send it to your teacher
Spiral review
Five questions from earlier units
0 / 5
1. (Unit 11) On a level rail, what is the slowing of a grind with μ = 0.30?
Why: a = μg = 0.30 times 9.8 = 2.94 m/s squared.
2. (Unit 10) Who was the first woman skater in Tony Hawk's Pro Skater?
Why: Elissa Steamer was the first woman in the 1999 game.
3. (Unit 11) Why should you approach a ledge at a shallow angle?
Why: Riding straight at it slams the board into the edge or over the top.
4. (Unit 10) How many degrees is two and a half full turns?
Why: 2.5 × 360 = 900 degrees.
5. (Unit 11) What is the safest bail when a grind stops short?
Why: Stepping off puts you on your feet without falling.
Send it to your teacher
Write it
Pick one move from this unit: a carve, a frontside 180 ollie, or pumping a bowl. Explain how to do it step by step, using front foot and back foot, and then explain the physics behind it with one worked example that shows every step of the arithmetic.
Start with the safety gear and the place you would practice.
Write the steps in order with First, Next, Then and Finally.
Name the physics idea: centripetal force, angular momentum or work and energy.
Show each number with its unit, such as m/s, kg or N.
End by explaining what a common mistake does to the physics.
0 wordsSaved on this device as you type.
For the teacher
Every lesson keeps its own three checks; a lesson is ticked when all three are right. Chapter reviews, the unit test and its spiral review (five questions from earlier units in this band) score on the page. When the site is connected to your sheet, or the link carries ?dest=, each one also has a Send box: the first-try score, the standards, the supports used, the attempt number and the minutes go to your sheet as an IEP data point.
Print this page for a paper copy of the readings, the sources, the words and the questions; the answers print as dashed boxes under each question.
Fact-check notes for this course live in the handoff: quotes marked (paraphrased) were set that way on purpose.