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

Options

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

Answer

C

Explanation

We know that `omega = 2 pi` n
`therefore " " omega_(1) = 2pi` n
where `n_(1)` = 1800 rpm `n_(2)` = 3000 rpm and `Delta = 20 s`

`omega_(1) = 2pi xx (1800)/(60) = 2pi xx 30 = 60pi`
similarly ,`omega _2=2pin_2 =2pixx(3000)/(60)=2pixx50=100pi``therefore" " alpha=("change in angular velocity")/("time interval")` `alpha=(omega_2-omega_1)/(Deltat)=(100pi-60pi)/(20)``(40pi)/(20)=2pirads^(-2)`