Question

The angular velocity of flywheel decreases uniformly from 12000rev/min to 3000 rev/min in 8 sec. Find theangular acceleration and the number of revolutions made by the wheel in the 8 sec interval. How many more seconds are required for the wheel to come to rest?

Answer 1

Given,

initial angular velocity, w_o = 12000 rev/min = 1256.63 rad/s

final angular velocity, w = 3000 rev/min = 314.16 rad/s

time taken, t = 8 sec

Let the angular acceleration be

using, w = w_o + t

314.16 = 1256.63 + *8

= -117.808 rad/s²

-ve sign denotes that the flywheel is stopping

again, for angular displacement, using,

= w_ot - 0.5*t² = 1256.63*5 - 0.5*117.808*5²

= 4810.55 rad

Again, for it to stop,

initial angular velocity, w_o = 3000 rev/min = 314.16 rad/s

final angular velocity, w = 0 rad/s

using, w = w_o + t'

314.16 = 1256.63 - 117.808*t'

t = 8 s

that is 8 more seconds are required for it to come to rest