A playground merry-go-round has radius `2 m` and moment of inertia `2000 kg m^(2)` about a vertical axle through its center.
(a) A boy applies `50 N` force tangentially to the edge of the merry-go-round for `20 s`. If the merry-go-round is initially at rest, what is its angular speed after `20 s`?
(b) How much work did the boy do on the merry-go-round?
(c) What is the average power supplied by the child?
(d) What is the instantaneous power supplied by the child at `t=20 s`?

Explanation

(`a`)
`tau_(0)=FR=I_(0)alpha`
`50xx2=2000alpha implies alpha=(1)/(20) rad//s^(2)`
`omega=omega_(0)+alpha t=0+(1)/(20)xx20= 1 rad//s`
(b) `theta=omega_(0)t+(1)/(2)alpha t^(2)=0+(1)/(2)xx(1)/(20)(20)^(2)=10 rad`
`W=tau_(0) theta=100xx10=1000J`
(c) `barP=(W)/(t)=(1000)/(20)=5W`
(d) `P=tau omega=100xx1=100W`