Question

A wheel of diameter 40cm started from rest and attains a speed of 240 RPM in 4 minute calculate its angular displacement within this time interval​

Answer 1

initial angular velocity, $\omega_0$ = 0

final angular velocity, $\omega$ = 240 rpm

= 240 × 2π/60 = 8π rad/s

average angular velocity, $\omega_{av}=\frac{\omega_0+\omega}{2}$

$\omega_{av}=\frac{0+8\pi}{2}=4\pi$

[ we know, 1 rpm = 2π/60 rad/s ]

time taken, t = 4 min = 240 sec

angular displacement, $\theta=\omega_{av}t$

= 4π × 240 = 960π rad

hence, angular displacement is 960π