First slide

Rolling motion

Question

In the figure, the velocities are in ground frame and the cylinder is performing pure rolling on the plank, velocity of point 'A' would be

Moderate

A

$2 v_{C}$
B

$2 v_{C} + v_{P}$
C

$2 v_{C} - v_{P}$
D

$2 (v_{C} - v_{P})$

Solution

For pure rolling velocity of the point of contact has to be equal to the velocity of the surface.
Let us say cylinder rolls with angular velocity $ω .$
At point B,
$v_{C} - ω r = v_{P} \Rightarrow ω r = v_{C} - v_{P}$
At point A,
$v_{A} = v_{C} + ω r = 2 v_{C} - v_{P}$

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