Question

A wheel starts from the rest and attains an angular velocity of 20 radian/s after being uniformly accelerated for 10 s.The total angle in radian through which it has turned in 10 second is

• A. $20\pi$
• B. $40\pi$
• C. $100$
• D. $100\pi$

Answer 1

The correct option is C $100$

From kinematics laws for rotational motion:

$\omega ={\omega }_0+\alpha t$ ..(1)

$\theta ={\theta }_0+{\omega }_{0}t+\frac{1}{2}\alpha t^2$....(2)

${\omega }^2-{\omega }_0^2=2\alpha \theta$.....(3) where,

$\omega$ is final angular velocity

${\omega }_0$ is initial angular velocity

$\theta$ is angular displacement

$\alpha$ is angular acceleration and $t$ is time

From(1) , $20=0+\alpha \times 10$

$\alpha =2rad/s^2$

From(3) , $(20{)}^2-0^2=2\times 2\times \theta$

$400=4\theta$

$\theta =100rad$