A rotating wheel changes angular speed from 1800 rpm to 3000 rpm in 20 s. What is the angular acceleration assuming to be uniform ?

Options

A. `2 pi " rad " s^(-2)`
B. `60 pi "rad" s^(-2)`
C. `40 pi "rad" s^(-2)`
D. `90 pi "rad "s^(-2)`

Answer

A

Explanation

Here,
Initial angular speed of the wheel,
`omega_(0)=1800xx(2 pi)/(60) "rad" s^(-1)= 60 pi "rad s"^(-1)`
Final angular speed of the wheel,
`omega = 3000xx(2pi)/(60) "rad" s^(-1)= 100 pi "rad" s^(-1)`
Time during which this change of speed takes place, `t=20` s
Let `alpha` be angular acceleration of the wheel.
As `omega= omega_(0)+ alpha t`
`:.alpha= (omega-omega_(0))/(t)= (100 pi - 60 pi)/(20)" rad" s^(-2)`
`= 2pi "rad"s^(-2)`