One symmetry, one conserved quantity

Science · Forces & Motion · ages 22-24

Name ______________________ Date ____________

A spinning skater pulls her arms in while no external torque acts. What happens to her rate of spin?
- It rises, as her moment of inertia shrank
- It falls, because she stopped pushing
- It stays the same, because nothing pushed her
Which continuous symmetry of the action gives conservation of momentum?
- Rotation of the setup
- Rescaling all lengths by a factor
- Translation of the setup in space
The angular momentum of a system stays constant whenever no net external torque acts on it.
Circle one: True False
You check an action and find it unchanged when the whole experiment is run one hour later. Which quantity is conserved?
- Angular momentum
- Energy
- Electric charge
A football player runs into the goalpost and bounces backward. The Earth recoils by an immeasurably small amount. What does this show?
- Momentum was destroyed in the collision
- Total momentum stayed constant across player and Earth
- Only the lighter body carries momentum
A spinning top slows over minutes because bearing friction applies a small torque. What happens to its angular momentum?
- It holds exactly fixed
- It slowly drifts downward
- It grows to compensate
A wheel has moment of inertia 2 and angular velocity 3, and its angular momentum is L equals I times omega. Type the value of L.
Answer: ______________
A student says the skater spins faster because pulling her arms in applies a torque that pushes her around. What is wrong with this?
- Angular momentum is not defined for a skater
- Nothing: a torque is exactly what speeds her up
- Pulling arms in shrinks her radius, and spin rate follows from fixed L with no torque needed

Answer key

For grown-ups. Fold this page away before handing over the rest.

One symmetry, one conserved quantity W1-mt_kAoOn8syBK-s1

It rises, as her moment of inertia shrank · L equals I times omega stays fixed, so a smaller I forces a larger omega.
Translation of the setup in space · Shifting everything in space changes nothing, and that symmetry conserves momentum.
True · Without outside torque there is nothing to change L, so initial equals final.
Energy · A shift in time is the symmetry behind energy conservation.
Total momentum stayed constant across player and Earth · Internal forces move momentum between parts, so the player's loss is the Earth's gain.
It slowly drifts downward · The symmetry is only approximate now, so L is only nearly conserved and drifts.
6 · Multiply moment of inertia by angular velocity: 2 times 3 is 6.
Pulling arms in shrinks her radius, and spin rate follows from fixed L with no torque needed · No external torque acts, so the faster spin comes from a smaller I at fixed L.