A wheel of mass 20 ~kg and radius 30 ~cm is rotating at an angular speed of 80 rev / min when the motor 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 5 rev.

Step-by-step solution

Given that, mass of wheel, m=20 ~kg Radius, R=30 ~cm =30 10⁻² ~m Initial angular speed, aligned ₀ & =80 rpm = 80 2 60 & = 8 3 rad / s aligned Angular displacement, =2 (number of revolution) =2 5=10 rad Final angular speed, =0 By equations of rotational kinematics. Angular acceleration, = ^2- ₀^2 2 Substituting the given values, we get aligned & = 0- ( 8 3 )^2 2 10 rad / s ^2 & =- 16 45 rad / s ^2 aligned Now, the tangential force will act opposite to the direction of rotation of wheel which will provide necessary r