Awheel free to rotate about its axis that is not frictionless is initially at rest. a constant external torque of +46 n·m is applied to the wheel for 17 s, giving the wheel an angular velocity of +580 rev/min. the external torque is then removed, and the wheel comes to rest 120 s later. (include the sign in your ) find the moment of inertia of the wheel.(b) find the frictional torque, which is assumed to be constant.

Explanation:

Let Torque due to friction be

F  

Net torque

= 46 - F

Angular impulse = change in angular momentum

=(  46 - F ) x 17  = I X 580

When external torque is removed , only friction creates torque reducing its speed to zero in 120 s so

Angular impulse = change in angular momentum

F  x 120 = I X 580

(  46 - F ) x 17 = F  x 120

137 F = 46 x 17

F = 5.7 Nm

b )

Putting this value in first equation

5.7 x 120 = I x 580

I = 1.18 kg m²

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