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Q.
A wheel whose moment of inertia is $2\, kg\, m^2$ has an initial angular velocity of $50\, rad\, s^{-1}$. A constant torque of 10 N m acts on the wheel. The time in which the wheel is accelerated to $80\, rad\, s^{-1}$ is
JIPMERJIPMER 2015System of Particles and Rotational Motion
Solution:
Initial angular velocity = $50\, rad\, s^{-1}$.
Final angular velocity = $80\, rad\, s^{-1}$,
Torque = $10\, N\, m$
Moment of inertia =$2\, kg\, m^2$
Angular acceleration $\alpha$ is given by $\tau = I \alpha$
$\alpha = \frac{\tau}{I} = \frac{10}{2} = 5 \, rad \, s^{-2}$
Hence if $t$ is the time,
$5t = 80 -50 = 30 \:\:\: \Rightarrow \:\: t = 6 \,s$