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. `2pi 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) = 1800 xx (2pi)/(60) "rad" s^(-1) = 60 pi rad s^-1`
Final angular speed of the wheel ,
`omega= 3000 xx (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 .
`therefore alpha = (omega - omega_(0)) /(t) = (100 pi - 60 pi)/(20) rad s^(-2) = 2pi rad s^(-2)`