Question

a wheel starts rotating from rest and attains an angular velocity of 60 rad/sec in 5 second the total angular displacement in radiant will be

Answer 1

here is your answers

Answer 2

Explanation:

It is given that,

Initial speed of wheel, $\omega_i=0$

Final angular velocity of wheel, $\omega_f=60\ rad/s$

Time taken, t = 5 s

Let $\alpha$ is the angular acceleration of the wheel. It is calculated as :

$\alpha=\dfrac{\omega_f-\omega_i}{t}$

$\alpha=\dfrac{60}{5}$

$\alpha=12\ rad/s^2$

Let $\theta$ is the angular displacement of the wheel. It can be calculated using second equation of motion as

$\theta=\omega_i t+1/2 \alpha t^2$

$\theta=0+1/2\times 12\times 5^2$

$\theta=150$

Hence, this is the required solution.