Questions: Rotational Kinematics

Question 1

A disk is rotating at constant angular velocity. Point A is on the rim; Point B is halfway between the center and the rim. Which statement is true?

• A. A and B have the same tangential speed
• B. A and B have the same angular velocity
• C. A has a smaller angular velocity than B
• D. B has a greater tangential speed than A

Answer: (B)

Angular velocity ω describes how fast the angle is changing — every point on a rigid rotating body sweeps through the same angle per second, so ω is the same for all points. Tangential speed, however, depends on radius: v = rω, so point A on the rim (larger r) moves faster through space than point B closer to the center.

Question 2

The kinematic equation ω = ω₀ + αt can be applied to any spinning object as long as you know its initial angular velocity.

• T. True
• F. False

Answer: False

This equation — and all four constant-acceleration kinematic equations — require that the angular acceleration α is constant throughout the motion. If α varies (for example, as torque changes), these equations give incorrect results. This is the direct rotational analogue of the linear restriction: v = v₀ + at only holds when acceleration is constant.

Question 3

A point on the rim of a wheel of radius r is moving at tangential speed v. What is the wheel's angular velocity ω, and what are its units?

Model answer: ω = v/r, in radians per second (rad/s)

The arc-length relationship v = rω can be rearranged to ω = v/r. Angular velocity is measured in rad/s because radians are dimensionless (arc length divided by radius), leaving units of inverse seconds. This relationship is the bridge between the rotational and linear descriptions of the same physical motion.