Question

A wheel turns through an angle of 188 radians in 8.0 s; and its angular speed at the end of the period is 44 rad/s. If the angular acceleration is constant, what was the angular speed of the wheel at the beginning of the 8.0 s interval?

Answer 1

Answer:

3 rad/s

Explanation:

$\omega_f$ = Final angular velocity = 44 rad/s

$\omega_i$ = Initial angular velocity

$\theta$ = Angle of rotation = 188 radians

t = Time taken

Angular displacement is given by

$\theta=\frac{\omega_i+\omega_f}{2}\times t\\\Rightarrow \omega_i+\omega_f=\frac{\theta\times 2}{t}\\\Rightarrow \omega_i=\frac{\theta\times 2}{t}-\omega_f\\\Rightarrow \omega_i=\frac{188\times 2}{8}-44\\\Rightarrow \omega_i=47-44\\\Rightarrow \omega_i=3\ rad/s$

The initial velocity is 3 rad/s