Question

# A body rotates about a fixed axis with an angular acceleration of $$1\ rad/sec^2$$. Through what angle does it rotate during the time in which its angular velocity increases from $$5 rad/s$$ to $$15 rad/s$$.

Solution

## Given:The angular acceleration of the body is $$\alpha =1\ rad/s^2$$The initial angular velocity of the body is $$\omega_0=5\ rad/s$$The final angular velocity of the body is $$\omega =15\ rad/s$$The final angular velocity of the body can be obtained as:$$\therefore w=w_0+\alpha t$$$$t=\dfrac{\omega -\omega_0}{ \alpha}$$Substitute the values:$$t =\dfrac{15-5}{1}=10\ sec$$The angular displacement of the body is given by:$$\theta=\omega_0t +\dfrac12\alpha t^2$$$$\theta=5\times 10+\dfrac12\times 1\times 100$$$$=100\ rad.$$Physics

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