A wheel of mass 10 kg and radius 20 cm is spinning at an angular speed of 100 rev/min when the motor is switched off. Ignoring friction at the axle, determine the force that must be applied tangentially to the wheel to bring it to a halt in 10 revolutions.

Step-by-step solution

Given the initial angular speed of the wheel: ₀ = 100 rev/min = 100 2 60 = 10 3 rad/s The final angular speed is = 0 . The angular displacement to bring the wheel to a halt is: = 10 rev = 10 2 = 20 rad Using the kinematic equation for rotational motion: ^2 = ₀^2 + 2 Substituting the values: 0 = ( 10 3 )^2 + 2 (20 ) 0 = 100 ^2 9 + 40 = - 100 ^2 9 40 = - 5 18 rad/s ^2 Assuming the wheel to be a solid disc, its moment of inertia is: I = 1 2 mR^2 The magnitude of the required torque is: = I| | = ( 1 2 mR^2 ) ( 5 18 ) S