A wheel 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 answers.) (a) Find the moment of inertia of the wheel. (b) Find the frictional torque, which is assumed to be constant.

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Physics

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23 June, 05:43

A wheel 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 answers.) (a) Find the moment of inertia of the wheel. (b) Find the frictional torque, which is assumed to be constant.

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Miguel Jenkins · Answer 1

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