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  4. A torque of 30 N-m is acting on a wheel of mass 5 kg and moment of inertia 2 kg-m2. If wheel starts rotating from rest then, its angular displacement in 10 seconds will be:

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Q. A torque of $30 \,N-m$ is acting on a wheel of mass $5 \,kg$ and moment of inertia $2\, kg-m2$. If wheel starts rotating from rest then, its angular displacement in $10 $ seconds will be:

Rajasthan PMTRajasthan PMT 2002Motion in a Plane

Solution:

$\tau =I \alpha $
$30 =2 \times \alpha $
$\Rightarrow \alpha =15\, rad / sec ^{2}$
From equation of angular motion
$\theta=\omega_{0} t+\frac{1}{2} \alpha t^{2}$
$=0+\frac{1}{2} \times 15 \times 10 \times 10$
$=750\, rad$