Compare static and kinetic friction in rolling motion.
Static friction: No relative motion at contact point, no energy dissipation. Kinetic friction: Relative motion at contact point, energy dissipation.
What are the key differences between rolling with and without slipping?
Without slipping: $v = r\omega$ applies, static friction, no energy loss. With slipping: $v = r\omega$ does not apply, kinetic friction, energy loss.
Compare the point of contact in rolling with and without slipping.
Without slipping: contact point is momentarily at rest. With slipping: contact point has relative motion.
What is the effect of kinetic friction on a rolling object?
It dissipates energy, reducing both translational and rotational kinetic energy, and slows the object down.
What happens when an object begins to slip while rolling?
Kinetic friction comes into play, energy is dissipated, and the linear and rotational motions become decoupled.
What is the effect of increasing the moment of inertia on a rolling object's speed down an incline?
An object with a larger moment of inertia will have a lower linear speed at the bottom of the incline, as more energy is stored in rotational kinetic energy.
What is the effect of static friction on a rolling object that is not slipping?
It provides the necessary force for rolling without losing energy; the contact point is momentarily at rest, so static friction doesn't dissipate energy.
What happens to the velocity of the point at the top of a rolling object (without slipping)?
The velocity of the point at the top of the rolling object is twice the velocity of the center of mass.
Define translational kinetic energy.
Energy due to the motion of an object's center of mass, depending on its mass and velocity.
Define rotational kinetic energy.
Energy due to an object's spinning, depending on its moment of inertia and angular velocity.
Define rolling without slipping.
A type of motion where there's a direct relationship between an object's linear and rotational motions.
Define rolling with slipping.
A type of motion where an object's linear and rotational motions are no longer directly related, and kinetic friction dissipates energy.
Define static friction in the context of rolling motion.
The force that allows an object to roll without slipping; it does no work and doesn't dissipate energy.
Define kinetic friction in the context of rolling motion.
The force that dissipates energy when an object slips while rolling, doing negative work and reducing total kinetic energy.
