A wheel on a game show is given an initialangular speed of 1.25 rad/s. It comes

Question

A wheel on a game show is given an initialangular speed of 1.25 rad/s. It comes to rest after rotatingthrough 3/4 of a turn.
(a) Find the average torque exerted on the wheel given that it is adisk of radius 0.72 m and mass 6.4 kg.
...... N·m
(b) If the mass of the wheel is halved and its radius is doubled,will the angle through which it rotates before coming to restincrease, decrease, or stay the same?
......
Explain. (Assume that the average torque is unchanged.) A wheel on a game show is given an initialangular speed of 1.25 rad/s. It comes to rest after rotatingthrough 3/4 of a turn.
(a) Find the average torque exerted on the wheel given that it is adisk of radius 0.72 m and mass 6.4 kg.
...... N·m
(b) If the mass of the wheel is halved and its radius is doubled,will the angle through which it rotates before coming to restincrease, decrease, or stay the same?
......
Explain. (Assume that the average torque is unchanged.)

Explanation / Answer

     = 2 - o2 /2
   where = (3/4) 2 and = 0
   = 0.1657 rad/s^2
  Average torque is
      =I
where I = (1/2) MR2   
   =(1/2)MR2
   =0.275Nm
b) When the mass is halved and radius is doubledthen moment of inertia is doubled. As there is no change in theaverage torque, the angular accelerationsdecreases.   
     

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