Question

a grinding stone of radius 2m revolving at 120 rpm accelerates to 660 r.p.m.in 9 seconds. find the angular acceleration and linear acceleration?

Answer 1

initial angular velocity , $\omega_0$ = 120rpm = 120 × 2π/60 = 4π rad/s 
final angular velocity, $\omega$= 660rpm = 660 × 2π/60 = 22π rad/s 
radius of circular path, r = 2m 
time taken , t = 9 sec 

use formula, $\omega=\omega_0+\alpha t$ 
22π = 4π + $\alpha$ × 9
2π = $\alpha$

hence, angular acceleration is 2π rad/s² 

linear acceleration, $a=r\alpha$
= 2 × 2π = 4π m/s² = 12.56 m/s²