An electric motor exerts a constant torque of =10Nm on a grindstone mounted on i

Question

An electric motor exerts a constant torque of =10Nm on a grindstone mounted on its shaft; the moment of inertia of the grindstone is I=2.0kgm2. If the system starts from rest, find the work done by the motor in 8.0 s and the kinetic energy at the end of this time. What was the average power delivered by the motor?

Part A

Suppose we now turn off the motor and apply a brake to bring the grindstone from its greatest angular speed of 54 rad/s to a stop. If the brake generates a constant torque of 17 Nm , find the total work done (including signs) needed to stop the grindstone.

Answer: -2916 J Part B

Part B

Find the average power (including signs) needed to stop the grindstone in Part A.

Need help with Part B

Explanation / Answer

Torque T = I A

where I is moment of inertial and A is angular accleration

so A = T/A = 10/2 = 5 rad/s^2

Work Done W = change in KE = IW^2

angular velocity W = At = 5* 8 = 40 rad/s

so

KE = WOrk Done W =0.5 IW^2

W = 0.5 * 2* 40*40

W = 1600 Joules

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Power P = W/t = 1600/8 = 200 Watts

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Wo = 21 rad/s Wo = 50 rad/s

Ang accleration a = T/I = 13/2 = 6.5 rad/^2

Work Done W = 0.5 IW^2

W = 0.5 * 2 * 21*21

W = 441 J

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Power P = 441/8 = 55.12 Watts

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