Rotation, Torque, and Angular Momentum
Angular Quantities
Rotation analogs
Rotational motion mirrors linear motion. Angular displacement , angular velocity , and angular acceleration play roles analogous to position, velocity, and acceleration.
Linear-rotational analogies
Torque and Equilibrium
Torque definition
Torque measures the turning effect of a force: . A larger lever arm or a perpendicular force creates more turning influence.
When is torque maximized for a given force and lever arm?
Torque depends on , which is maximized at .
Correct answer: When force is perpendicular to the lever arm
What condition defines rotational equilibrium?
If the net torque is zero, angular acceleration is zero and the object does not begin rotating faster.
Correct answer: Net torque equals zero
Moment of Inertia and Angular Momentum
Rotational resistance
Moment of inertia depends on how mass is distributed relative to the axis. Objects with mass farther from the axis are harder to spin up or slow down.
Angular momentum
Angular momentum is for a rigid body rotating about a fixed axis. When external torque is negligible, angular momentum is conserved, which explains why figure skaters spin faster when pulling in their arms.
If a spinning object pulls mass closer to its axis and no external torque acts, what happens to angular speed?
With angular momentum conserved, a smaller moment of inertia means a larger angular speed.
Correct answer: It increases
Why does mass distribution matter for rotational motion?
Mass farther from the axis increases , making rotation harder to change.
Correct answer: It changes the moment of inertia