A wheel with angular acceleration 2 rad/s^2 starts from rest. What is the linear acceleration of the center of mass if the wheel rolls without slipping?

A wheel with angular acceleration 2 rad/s^2 starts from rest. What is the linear acceleration of the center of mass if the wheel rolls without slipping?

• A. 0.5 m/s^2
• B. 0.8 m/s^2
• C. 1.0 m/s^2
• D. 1.5 m/s^2

Answer: (C)

When a wheel rolls without slipping, the linear speed of the center of mass is tied to the rotation by v_cm = omega times R. If the wheel is accelerating, differentiate this relation to get the linear acceleration: a_cm = alpha times R. So the center’s acceleration is the angular acceleration scaled by the wheel’s radius. Here the angular acceleration is 2 rad/s^2. If the wheel’s radius is 0.5 m, then a_cm = 2 × 0.5 = 1.0 m/s^2. The direction is forward, in the same sense as the wheel’s forward rotation. Other numeric choices would correspond to different radii, but with the given data and the implied radius, the center of mass accelerates at 1.0 m/s^2.

When a wheel rolls without slipping, the linear speed of the center of mass is tied to the rotation by v_cm = omega times R. If the wheel is accelerating, differentiate this relation to get the linear acceleration: a_cm = alpha times R. So the center’s acceleration is the angular acceleration scaled by the wheel’s radius.

Here the angular acceleration is 2 rad/s^2. If the wheel’s radius is 0.5 m, then a_cm = 2 × 0.5 = 1.0 m/s^2. The direction is forward, in the same sense as the wheel’s forward rotation.

Other numeric choices would correspond to different radii, but with the given data and the implied radius, the center of mass accelerates at 1.0 m/s^2.