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

Answer

C

Explanation

We know that, `omega=2pir" "therefore_(1)=2pin_(1)`
where, `n_(1)=1800 "rpm", n_(2)=3000"rpm", Deltat=20s`
`omega_(1)=2pixx(1800)/(60)=2pixx30=60pi`
Similarly , `omega_(2)=2pin_(2)=2pixx(3000)/(60)=2pixx50=100pi`
If the angular velocity of a rotating wheel about an axis is changed by change in angular velocity in a time interval `Deltat`, then the angular acceleration of rotating wheel about that axis is given by
`alpha=("Change in angular velocity")/("Time interval")`
`=(omega_(2)-omega_(1))/(Deltat)=(100pi-60pi)/(20)`
`=(40pi)/(20)=2pi"rad s"^(-2)`