Question

Consider a disc rolling without slipping on a horizontal surface at a linear speed V as shown in figure:

• A. the speed of the particle A is 2V.
• B. the speed of B, C and D are all equal to V.
• C. the speed of C is zero.
• D. the speed of O is less than the speed of B.

Answer 1

Answer: (A), (C), (D)

The correct options are
A the speed of the particle A is 2V.
C the speed of C is zero.
D the speed of O is less than the speed of B.

For pure rolling,
$v=\omega r$
Point A:
$v_A=\omega r+v_{cm}=\omega r+\omega r=2\omega r$ since velocity of cm $v_{cm}=\omega r$
Point C:
$v_C=-\omega r+v_{cm}=-\omega r+\omega r=0$ since point C is at rest.
Point B:
$\overrightarrow{v_B}=-\hat{j}\omega r+\hat{i}{v}_{cm}=-\hat{j}\left(\omega r\right)+\hat{i}\left(\omega r\right)$
$\therefore \left|\overrightarrow{v_B}\right|=\sqrt{(\omega r{)}^2+(\omega r{)}^2}=\sqrt{2}\omega r$
$v_O=v_{cm}=\omega r$