Question

A body rotates about a fixed axis with an angular acceleration 1rad//s^(2) through what angle does it rotates during the time in which its angular velocity increases from 5rad//s to 15rad//s?

Answer 1

The angle of rotation = 100 radians

Step by step explanation:

Given details :

Angular acceleration α = 1 $\frac{rad}{s^2}$

Initial velocity u =  5 $\frac{rad}{s}$

Final velocity v =15 $\frac{rad}{s}$

In case of linear motion:

One equation of motion =

$v^2 = u^2 + 2\times a \times s$                  

So,

$s = \frac{(v^2 - u^2)}{2\times a}$           ( where s is the distance covered )       (equation 1)

Similarly In case of angular motion:

acceleration a changes to angular acceleration  α.

and distance s changes to angular distance (angle)   θ.

So, the equation of angular motion becomes

$\theta = \frac{(v^2 - u^2)}{2\alpha }$                                                                            (equation 2)

Putting the values given of  u, v and   α.

$\theta = \frac{(15^2 - 5^2)}{2\times 1 }\\\\\theta = \frac{(200)}{2 }$

$\textbf{\Large So, The angle of rotation = 100 radians }$