A wheel of mass 10 kg and radius 0.2 m is rotating at an angular speed of 100 rpm, when the motion is turned off. Neglecting the friction at the axis. Calculate the force that must be applied tangentially to the wheel to bring it to rest in 10 rev. Assumed wheel to be a disc.

Explanation

`omega=100 rev/min`
`=5/3rev/s=(10pi)/3rad/s`
`theta=10 rev.=20pirad`
`r=0.2m`
After 10 revolutions the wheel wil come to rest by as tangential force.
Therefore the angular deceleration produced by the force
`=K=(K2)/(2K)`
therefore the torque by which the wheel will come to an rest `=IcmxxK`
`implies Fxxr=I_(cm)xx alpha`
`rarr Fxx0.2=1/2mr^2x((10pi/3)62(2xx20pi)`
`rarr F=1/2xx10xx0.2xx(10pi^2)/((9xx2xx20pi))`
`=(5pi)/18=15.7/18=0.87N`