A flywheel of moment of inertia `10kg m^(2)` is rotating at `50 rad//s`. It must be brought to stop in `10 s`.
(a) How much work must be done to stop it?
(b) What is the required average power?

Explanation

Given, `omega_(0)=50 "rad/s",t=10s`
From the equation, `omega=omega_(0)=alphat`
`0=50-alphaxx10`
`alpha=5 "rad/s"^(2)`
Again, `theta =omega_(0)t-(1)/(2)alphat^(2)`
`=50xx1-(1)/(2)xx5xx(10)^(2)`
`=500-250=250 "rad"`
Retarding torque, `tau=I alpha=10xx5=50` cm
Work done by retarding torque
`W=tau theta=50xx250=12500 `J
Required average power,
`P=(W)/(t)=(12500)/(10)=1250W`.