An electric motor rotating a workshop grinding wheel at 1.00 3 102 rev/min is switched off. Assume the wheel has a constant negative angular acceleration of magnitude 2.00 rad/s2. (a) How long does it take the grinding wheel to stop? (b) Through how many radians has the wheel turned during the time interval found in part (a) ?

(a) 5.25 second

(b) 27.5625 rad

Explanation:

fo = 1.003 x 10^2 rev / min = 1.672 rev / sec

ωo = 2 x 3.14 x fo = 2 x 3.14 x 1.672 = 10.5 rad/s

α = - 2 rad/s^2

(a) Let t be the time taken to stop.

ω = 0 rad/s

Use first equation of motion for rotational motion

ω = ωo + α t

0 = 10.5 - 2 x t

t = 5.25 second

(b) Let it rotates by an angle θ in the given time.

use third equation of motion for rotational motion

ω² = ωo² + 2 α θ

0 = 10.5 x 10.5 - 2 x 2 x θ

θ = 27.5625 rad