First slide

Rolling motion

Question

A cylindrical drum, pushed along by a board rolls forward on the ground. There is no slipping at any contact. The distance moved by the man who is pushing the board, when axis of the cylinder covers a distance L will be

Moderate

A

L
B

2L
C

$π$ L
D

8 $πL$

Solution

Let $v_{0}$ be the linear speed of the axis of the cylinder and $ω$ be its angular speed about the axis. As it does not slip on the ground hence $ω = \frac{v_{0}}{R}$ . Where R is the radius of the cylinder.
Speed of the topmost point is v = $v_{0} + ωR = 2 v_{0}$
Since time taken by the axis to move a distance L is equal to t = $\frac{L}{v_{0}}$ .
In the same interval of time distance moved by the topmost point is $S = 2 v_{0} \times \frac{L}{v_{0}} = 2 L$

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