Question

A wheel is at rest. Its angular velocity increases uniformly and becomes $80$ radian per second after $5$ seconds. The angular displacement is:

• A. $800\text{rad}$
• B. $400\text{rad}$
• C. $200\text{rad}$
• D. $100\text{rad}$

Answer 1

The correct option is C $200\text{rad}$

It is given that the angular velocity$\left(\omega \right)$ increases uniformly . The angular acceleration$\left(\alpha \right)$ must be constant.

As it starts from rest and given that final angular velocity is $80\text{rad/sec}$ in $5\text{sec}$

${\omega }_i=0;{\omega }_f=80\text{rad/sec}$
$t=5\text{sec}$

By the equation of circular motion,
${\omega }_f={\omega }_i+\alpha t\Rightarrow \alpha =\frac{80}{5}=16{\text{rad/sec}}^2$

and the total angular displacement is ,
$\theta =\frac{1}{2}\alpha t^2=\frac{1}{2}\times 16\times 25=200\text{rad}$ as $({\omega }_o=0)$

Hence option C is the correct answer