Question

At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s. Two seconds later it has turned through 5.0 complete revolutions. What is the angular acceleration of this wheel?

Answer 1

As per condition of constant angular acceleration we can use kinematics

so here we will have

$\theta = \omega_i t + \frac{1}{2}\alpha t^2$

here we know that

$\theta = 5(2\pi) = 10\pi rad$

$\omega_i = 2 rad/s$

t = 2 s

$10\pi = 2(2) + \frac{1}{2}\alpha(2^2)$

$\alpha = 13.7 rad/s^2$

so above is angular acceleration of the wheel