First slide

Torque

Question

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ?

Moderate

A

$0.25 {rads}^{- 2}$
B

$25 {rads}^{- 2}$
C

$5 m s^{- 2}$
D

$25 m s^{- 2}$

Solution

$m = 3 kg, r = 40 cm = 40 \times 10^{- 2} m, F = 30 N$
Moment of inertia of hollow cylinder about its axis
$= m r^{2} = 3 kg \times (0.4)^{2} m^{2} = 0.48 kg m^{2}$
The torque is given by,
$τ = I α$
where I = moment of inertia,
$α = angular acceleration$
$In the given case, τ = r F, as the force is acting$ $perpendicularly to the radial vector.$
$∴ α = \frac{τ}{I} = \frac{F r}{m r^{2}} = \frac{F}{m r} = \frac{30}{3 \times 40 \times 10^{- 2}} = \frac{30 \times 100}{3 \times 40} α = 25 {rads}^{- 2}$

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