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

Answer 2

angular acceleration and linear acceleration