1.

A fly wheel having a moment of inertia of 10^(7) g cm^(2) and revolving at the rate of 120 rpm is stopped by a brake in course of 5 seconds. Find the controlling torque.

Answer»

`2.51 xx 10^(7)` DYNE-cm
`5.21 xx 10^(7)` dyne-cm
`1.25 xx 10^(7)` dyne-cm
`2.15 xx 10^(5)` dyne-cm

Solution :Obviously, the controlling torque will produce a retardation of the fly wheel. Let a. be the angular retardation produced by the application of the torque.
Initial angular speed of the fly wheel,
`omega_(1)=(2pir)/60=(2pixx120)/60=4PI"rad"//"sec"`
Final angular speed = `omega_(2) = 0`, time= t = 5 sec.
Now, applying the FORMULA `omega_(2) = omega_(1) - alphat`, we get
`0=4pi-alphaxx5` or `alpha=(4pi)/5` rad/se`c^(2)`
We know, torque = moment of Inertia (I) `xx alpha`
`therefore` Torque, `tau=10^(7)xx(4pi)/5=2.51xx10^(7)` dyne cm


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