The spin drier of a washing machine revolving at`15 rps` slows down to `5 rps`, while making `50` revolutions. Find (a) angular acceleration and (b) time taken.

Explanation

Here, `n_(1) = 15 rps, n_(2) = 5 rps`
Angle traced in `50` revolutions, `theta = 50 xx 2pi rad`
As `omega_(2)^(2) - omega_(1)^(2) = 2 alpha theta`
`:. alpha = (omega_(2)^(2) - omega_(1)^(2))/(2 theta) = (4pi^(2) (n_(2)^(2) - n_(1)^(2)))/(2 theta)`
`alpha = (2pi^(2) (5^(2) - 15^(2)))/(100pi) = -4 pi rad//s^(2)`
From `omega_(2) = omega_(1) + alpha t`
`t = (omega_(2) - omega_(1))/(alpha) = (2pi (n_(2) - n_(1)))/(alpha) = (2pi (5 - 15))/(-4pi) = 5s`