Question

A wheel on a game show is given an initial angular speed of 1.22 rad>s. It comes to rest after rotating through 0.75 of a turn. (a) Find the average torque exerted on the wheel given that it is a disk of radius 0.71 m and mass 6.4 kg. (b) If the mass of the wheel is doubled and its radius is halved, will the angle through which it rotates before coming to rest increase, decrease, or stay the same? Explain. (Assume that the average torque exerted on the wheel is unchanged.)

Answer 1

a] torque = I*alpha where I is moment of inertia, alpha is angular acceleration,

= 0.5mr^2*(w^2/2theta) ...alpha is substituted from third equation of rotation

= 0.5*6.4*0.71^2*(1.22^2/(2*0.75*2pi))

= 0.25475 Nm

b] Torque = 0.5mr^2*(w^2/2theta)

Here, Torque, w are same, m is doubled, r is halved,

theta will become half,

Decrease