First slide

Rolling motion

Question

In the figure, a sphere of radius 2 m rolls on a plank. The accelerations of the sphere and the plank are indicated. The value of $α$ is

Moderate

A

$2 rad / s^{2}$
B

$4 rad / s^{2}$
C

$3 rad / s^{2}$
D

$1 rad / s^{2}$

Solution

As sphere rolls, the lowest point of the sphere should have the same acceleration as the plank.
$\begin{array}{l} Hence, a_{1} = α R - a_{2} \\ 2 = 2 α - 4 \Rightarrow α = 3 rad / s^{2} \end{array}$

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