A uniform disc of mass 500 kg and radius 2 metres is rotating at the rate of 600 rpm. What is the torque required to rotate the disc in the opposite direction with the same speed in a time of 100 seconds?

Options

A. `600 pi Nm`
B. `500 pi Nm`
C. `400 pi Nm`
D. `300 pi Nm`

Answer

C

Explanation

For the disc, `M=500kg, R=2m`
`therefore" "I=(MR^(2))/(2)=500xx(4)/(2)="1000 kg m"^(2)`
Its angular velocity, `omega=2pixx(600)/(60)=20pi "rad/s"`
To rotate the disc in the opposite direction with the same speed, the opposing torque must decrease its angular velocity from `20pi " rad/s"` to zero and then increase it from 0 to `20pi`.
Thus the change in angular velocity
`=20pi-(-20pi)=40pi" rad/s"`
`therefore" Angular acceleration "alpha=(domega)/(dt)=(40pi)/(100)=(4)/(10)pi`
`therefore" Opposing torque "=Ialpha=1000xx(4)/(10)="400 N-m"`