First slide

Dynamics of rotational motion about fixed axis

Question

A solid cylinder of mass 2 kg and radius 4 cm rotating about its axis at the rate of 3 rpm. The torque required to stop after 2 $π$ revolution is

Moderate

A

$2 \times 10^{6} Nm$
B

$2 \times 10^{- 6} Nm$
C

$2 \times 10^{- 3} Nm$
D

$12 \times 1 0^{- 4} Nm$

Solution

$ω_{0} = 3 rpm = 3 \times \frac{2 π}{60} rad / \sec = \frac{π}{10} rad / \sec$
Using, $ω^{2} = {ω_{o}}^{2} + 2 αθ$
$0^{2} = {(\frac{π}{10})}^{2} + 2 (α) (2 π \times 2 π)$
$α = - \frac{1}{800} rad / \sec^{2}$
Torque, $τ = I α = \frac{1}{2} \times 2 \times 0 . 04^{2} (- \frac{1}{800}) N - m = - 2 \times 10^{- 6} N - m$
Negative sign indicates that the applied torque is retarding in nature

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