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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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