A wheel with radius 0.5 m and angular velocity 6 rad/s is rolling without slipping. What is the linear velocity of the center of mass?

A wheel with radius 0.5 m and angular velocity 6 rad/s is rolling without slipping. What is the linear velocity of the center of mass?

• A. 3 m/s
• B. 1 m/s
• C. 6 m/s
• D. 0.5 m/s

Answer: (A)

For a wheel rolling without slipping, the center-of-mass speed is tied to the wheel’s rotation through v = ωR. The tangential speed at the rim (due to rotation) equals the speed the center must have to roll without slipping, so the center moves with v = ωR. Here, the radius is 0.5 m and the angular velocity is 6 rad/s, so v = 6 × 0.5 = 3 m/s. The center of mass thus moves forward at 3 meters per second.

For a wheel rolling without slipping, the center-of-mass speed is tied to the wheel’s rotation through v = ωR. The tangential speed at the rim (due to rotation) equals the speed the center must have to roll without slipping, so the center moves with v = ωR.

Here, the radius is 0.5 m and the angular velocity is 6 rad/s, so v = 6 × 0.5 = 3 m/s. The center of mass thus moves forward at 3 meters per second.