First slide

Rolling motion

Question

A rigid body of radius R, either hollow or solid, lies on a smooth horizontal surface. The body is pulled by a horizontal force acting tangentially from the highest point. The distance travelled by the body in the time in which it makes one full rotation is the same that it will make in one fulI rotation during pure rolling. The rigid body will be

Moderate

A

solid sphere
B

hollow sphere
C

circular disc
D

hollow cylinder

Solution

$τ = F \times R = I α$
$I n o n e f u l l r o t a t i o n, θ = 2 π = \frac{1}{2} α t^{2}$
$t^{2} = \frac{4 π}{α} = \frac{4 π I}{F R}$
$Linear acceleration, a = F / M$
$Distance travelled in one rotation = 2 π R (given)$
$= \frac{1}{2} a t^{2} = \frac{1}{2} \frac{F}{M} \cdot \frac{4 π I}{F R} = \frac{2 π I}{M R}$
$It gives I = M R^{2}$
$It is a hollow cylinder .$

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