A dics rotates about the central axis starting from rest and accelerates with constant angular accelertion. At one time, it is rotating at `10 rps` , `60` revoluting later, its angular speed is `15rps`. Calculate (i) angular acceleration (ii) time required to complate `60` revols (iii) the time required to reach `10 rev//sec` angular speed and (iv) number of revoluting from rest until the time the disc reaches `10rps` angular speed.

Explanation

Here, `omega_(0) = 10rps = 20 pi rad//s`
`theta = 60 revols = 60 xx 2 pi radian`
`omega = 15 rps = 15 xx 2 pi rad//s`
From `omega^(2) - omega_(0)^(2) = 2 alpha theta`
`alpha = (omega^(2) - omega_(0)^(2))/(2 theta) = ((30 pi)^(2) - (20 pi)^(2))/(2 xx 60 xx 2pi)`
`alpha = (500 pi^(2))/(240 pi) = (25)/(12) xx 3.14 rad//s^(2)`
`= 6.54 rad//s^(2)`
From `omega = omega_(0) + alpha t`
`t = (omega - omega_(0))/(alpha) = (30pi - 20 pi)/(6.54)`
`t = (10 xx 3.14)/(6.54) = 4.8 s`
(ii) In this case, `omega_(0) = 0, omega = 10 xx 2 pi rad//s`
` alpha = (omega - omega_(0))/(alpha) = (20pi - 0)/(6.54) = 9.6 s`
(iv) In this time, `theta = (omega^(2) - omega_(0)^(2))/(2 alpha) = ((20pi)^(2) - 0)/(2 xx 6.54) = (400pi^(2))/(13.08)`
Number of revolutions
`= (theta)/(2pi) = (400pi^(2))/(2pi xx 13.08) = 48.0`