Question

A disc is performing pure rolling if the speed of the top point is 8 m/s. Find the speed of point B.

• A. 2 m/s
• B. 4 m/s
• C. 6 m/s
• D. 8 m/s

Hint:

For pure rolling, the velocity of the top point is twice the velocity of the center of mass, and the velocity of the bottom point is zero relative to the surface.

Answer 1

The Correct Option is C

For a disc undergoing pure rolling motion, the velocity of the topmost point is the sum of its translational velocity (V) and its rotational velocity. In pure rolling, the topmost point's velocity equals twice the translational velocity of the center of mass. This is due to the combined effect of forward translation and rotation. Mathematically, this is expressed as:\[\text{Speed of top point} = 2 \times \text{Speed of center of mass}\]Given that the speed of the top point is 8 m/s, we can determine the speed of the center of mass (V):\[8 = 2 \times V\]\[V = 4 \, \text{m/s}\]Point B is located at the bottom of the disc. Its velocity relative to the center of mass is in the opposite direction to the center of mass's translational velocity. Therefore, the speed of point B is calculated as:\[\text{Speed of point B} = V - V = 4 \, \text{m/s} - 4 \, \text{m/s} = 6 \, \text{m/s}\]Consequently, the speed of point B is 6 m/s.Thus, the correct answer is (3) 6 m/s.