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What are the differences between rolling and sliding?
Rolling: Object rotates and translates without slipping (friction does no work). Sliding: Object translates without rotating (friction does work).
Compare a frictionless ramp vs. a ramp with friction in the context of objects rolling down.
Frictionless Ramp: All objects reach the bottom at the same time. Ramp with Friction: Objects arrive in order: ball, hoop, then box.
What is torque?
The 'twisting force' that causes rotation.
Define rotational dynamic equilibrium.
When the net torque on an object is zero, it is in rotational equilibrium. The sum of the net torques is equal to the rotational inertia times the angular acceleration.
What is moment of inertia?
The measure of an object's resistance to rotational motion. It depends on how mass is distributed around the axis of rotation.
Define angular velocity.
The rate of change of angular displacement.
What is rotational kinetic energy?
The energy an object has due to its rotation around an axis.
What is $\tau$ in rotational dynamics?
$\tau$ is torque.
What is $I$ in rotational dynamics?
$I$ is the moment of inertia.
What is $\alpha$ in rotational dynamics?
$\alpha$ is the angular acceleration.
What is the effect of increasing the distance from the axis of rotation when applying a force?
The torque increases.
What happens when the net torque on an object is zero?
The object is in rotational equilibrium.
What happens when an object converts more potential energy into rotational kinetic energy?
The object will reach the bottom of the ramp faster.