First slide

Rolling motion

Question

Velocity of the centre of a small cylinder is v. There is no slipping anywhere. The velocity of the centre of the larger cylinder is

Moderate

A

2v
B

v
C

$\frac{3 v}{2}$
D

none of these

Solution

In figure, C₁ and C₂ are IC (instantaneous centre of rotation) of the two cylinders. The cylinder can be considered as rotating about C₁ and C₂. In the absence of slipping between the plank and the cylinders, points A₁ and A₂ have the same velocity. Angular velocity of the larger cylinder $ω =$ $\frac{2 v}{4 R} = \frac{v}{2 R}$ .
$v_{CM} = (2 R) (\frac{v}{2 R}) = v$

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