What are the key differences between linear velocity ( $v$ ) and angular velocity ( $\omega$ )?

Linear Velocity ( $v$ ): The rate of change of linear position, depends on radius. | Angular Velocity ( $\omega$ ): The rate of change of angular position, uniform in a rigid system.

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What are the key differences between linear velocity ( $v$ ) and angular velocity ( $\omega$ )?

Linear Velocity ( $v$ ): The rate of change of linear position, depends on radius. | Angular Velocity ( $\omega$ ): The rate of change of angular position, uniform in a rigid system.

What are the key differences between linear acceleration ( $a$ ) and angular acceleration ( $\alpha$ )?

Linear Acceleration ( $a$ ): The rate of change of linear velocity, depends on radius. | Angular Acceleration ( $\alpha$ ): The rate of change of angular velocity, uniform in a rigid system.

Compare and contrast angular velocity and tangential velocity.

Angular Velocity: Rate at which an object rotates (rad/s), constant for all points on a rigid rotating object. Tangential Velocity: Linear speed of a point on a rotating object (m/s), depends on the radius.

Compare and contrast angular acceleration and tangential acceleration.

Angular Acceleration: Rate at which angular velocity changes (rad/s²), constant for all points on a rigid rotating object. Tangential Acceleration: Linear acceleration of a point on a rotating object (m/s²), depends on the radius.

What is the effect of applying a constant tangential force to the edge of a disk?

It causes the disk to experience angular acceleration and thus rotate with increasing angular velocity.

What is the effect of increasing the radius on the linear velocity of a point on a rotating object, given a constant angular velocity?

The linear velocity of the point increases.

What is the effect of a non-zero angular acceleration?

The angular velocity of the object changes over time.

What is the effect of applying a torque to an object?

It causes the object to experience angular acceleration.

What happens to the tangential acceleration if the angular acceleration increases?

The tangential acceleration increases proportionally, given a constant radius.

Define angular displacement ( $\theta$ ).

Angular displacement is the angle through which a point or object has been rotated in a specified direction.

Define angular velocity ( $\omega$ ).

Angular velocity is the rate of change of angular displacement with respect to time.

Define angular acceleration ( $alpha$ ).

Angular acceleration is the rate of change of angular velocity with respect to time.

Define tangential acceleration ( $a_T$ ).

Tangential acceleration is the linear acceleration of a point on a rotating object, tangent to the circular path.

Define 'rolling without slipping'.

Rolling without slipping is a type of motion where a rotating object moves along a surface without sliding; the point of contact between the object and the surface is instantaneously at rest.