Starting from rest, a wheel, with uniform acceleration, attains an angular velocity of 60 rad`cdot s^(-1)` at the end of 30 complete revolutions. What is the angular acceleration of the wheel?

Explanation

Initial angular velocity, `omega_(1) ` = 0 .
Angular displacement at the the end of 30 revolutions,
`theta = 30 xx 2pi = 60 pi ` rad
Final angular velocity, `omega_(2)` = 60 rad`cdot s^(-1)`
Now, from the equation
`omega_(2)^(2) = omega_(1)^(2) + 2 alpha theta`
`" "`( `alpha` = angular acceleration of the wheel )
we get, `(60)^(2) = 0 + 2 alpha xx 60 pi`
or, `" " alpha = (30)/(pi) = 9.55 " rad"cdot s^(-2)` .