A flywheel of mass 1 metric ton and radius `1 m` is rotating at the rate of `420` rpm. Find the constant retarding torque required to stop the wheel in `14` rotations, assuming mass to be concentrated at the rim of the wheel.

Explanation

Here, `m = 1` metric ton `= 100 kg`,
`r = 1m, n_(1) = (420)/(60)rps = 7 rps, tau = ?`
`n_(2) = 0, theta = 14` rotations `= 14 xx 2pi` radio
From `omega_(2)^(2) - omega_(1)^(2) = 2 alpha theta`
`(2 pi n_(2))^(2) - (2 pi n_(1))^(2) = 2 alpha theta`
`alpha = (4pi^(2)(n_(2)^(2) - n_(1)^(2)))/(2 theta)`
`= (4pi^(2)(0 - 7^(2)))/(2 xx 14 xx 2pi) = (-4 xx 49 pi^(2))/(56 pi)`
`alpha =- (49)/(14) xx (22)/(7) = - 11 rad//s^(2)`
When mass is concemtrated at the rim, momentum of inertia of flywheel,
`I = mr^(2) = 100(1)^(2) = 1000 kg m^(2)`
`tau = I alpha = 1000 (-11) =- 1000 Nm`
Negative sign indictes retarding torque.