First slide

Rolling motion

Question

Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration ‘a’ perpendicular to the axis of the cylinder. What is F_friction at point P? It is assumed that the cylinder does not slip

Moderate

A

Ma/3
B

Mg
C

Ma/2
D

Ma

Solution

$\large {a}'$ = Acceleration of the centre of cylinder relative to the rug. and α = angular acceleration of the cylinder.
$\large \therefore ma-f=ma{}'.....(1)$
$\large f.R=\left ( \frac 12mR^2 \right )\alpha.....(2)$
$\large {a}'=\alpha R......(3)$
solving, $\large f=\frac {ma}{3}$

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