First slide

Dynamics of rotational motion about fixed axis

Question

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions $s^{- 2}$ is

Moderate

A

25 N
B

50 N
C

78.5 N
D

157 N

Solution

Here, mass of the cylinder, M = 50 kg
Radius of the cylinder, R = 0.5 m
$Angular acceleration, α = 2 rev s^{- 2} = 2 \times 2 π rad s^{- 2} = 4 π {rads}^{- 2}$
$Torque, τ = T R$
Moment of inertia of the solid cylinder about its axis,
$I = \frac{1}{2} M R^{2}$
$∴ Angular acceleration of the cylinder$
$α = \frac{τ}{I} = \frac{T R}{\frac{1}{2} M R^{2}}$
$T = \frac{M R α}{2} = \frac{50 \times 0.5 \times 4 π}{2} = 157 N$

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