Question

A pulley has the shape of a uniform solid disc of mass `2 kg` and radius `0.5 m`. A string is wrapped over its rim and is pulled by a force of `2.5 N`. The pulley is free to rotate about its axis. Initially, the pulley is at rest. Find the angular velocity and angle rotated by pulley in `10 s`.

Answer 1

Moment of inertia of pulley
`I=(1)/(2)mR^(2)=(1)/(2)xx2xx(0.5)^(2)=0.25 kg m^(2)`
Torque produced by force about `O`
`tau_(o)=2.5xx0.5=Ialpha=0.25alpha`
`alpha=5 rad//s^(2)` (constant)
`omega=omega_(0)+alphat=0+5xx10=50 rad//s`
`theta=omega_(0)t+(1)/(2)alphat^(2)=0+(1)/(2)5xx(10)^(2)=250 rad`