Question

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

Answer 1

Given:

The angular acceleration of the body is $\alpha =1rad/s^2$

The initial angular velocity of the body is ${\omega }_0=5rad/s$

The final angular velocity of the body is $\omega =15rad/s$

The final angular velocity of the body can be obtained as:

$\therefore w=w_0+\alpha t$

$t=\frac{\omega -{\omega }_0}{\alpha }$

Substitute the values:

$t=\frac{15-5}{1}=10sec$

The angular displacement of the body is given by:

$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$

$\theta =5\times 10+\frac{1}{2}\times 1\times 100$

$=100rad.$