Question

A string is wrapped around the rim of a wheel of moment of inertia 0.20 kg-m^2 nd radius 20 cm. The wheel is free to rotate about it axis. Initially, thewheel is t rest. The string is now pulled by a force of 20 N. Find the angular velocity of the wheel after 5.0 seconds.

Answer 1

The torque applied to the wheel is
`Gamma =F.r=(20N)(0.20m)=4.0 N-m`.
the angular acceleration produced is
`alpha =Gamma/I=(4.0N-m)/(0.20kg-m^2)=20 rad/s^2`
The angular velocity after 5.0 seconds is
`omega=omega_0+alphat=(20rad/s^2)(5.0s)=100rad/s`