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  4. A pulley has the shape of a uniform solid disc of mass 2 kg and radius 0.5 m. A string is wrapped over its rim and is pulled by a force of 2.5 N. The pulley is free to rotate about its axis. Initially, the pulley is at rest. Find the angular velocity of pulley just after 10 s.

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Q. A pulley has the shape of a uniform solid disc of mass $2\, kg$ and radius $0.5\, m$. A string is wrapped over its rim and is pulled by a force of $2.5 \,N$. The pulley is free to rotate about its axis. Initially, the pulley is at rest. Find the angular velocity of pulley just after $10\, s$.Physics Question Image

Solution:

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Moment of inertia of pulley
$I =\frac{1}{2} mR ^{2}=\frac{1}{2} \times 2 \times(0.5)^{2}=0.25 \,kg\, m ^{2}$
Torque produced by force about $O$
$\tau_{0}=2.5 \times 0.5= I \alpha=0.25 \alpha$
$\alpha=5\, rad / s ^{2}($ constant $)$
$\omega=\omega_{0}+\alpha t =0+5 \times 10=50\, rad / s$