Question

The flywheel of a motor has a mass of 300kgand a moment of inertia of 580kg⋅m2. The motor develops a constant torque of 2000N⋅m and the flywheel starts from rest.

Part A

What is the angular acceleration of the flywheel?

Express your answer in radians per second squared.

Part B

What is its angular velocity after it makes 4.00 revolutions?Express your answer in radians per second.

Part C

How much work is done by the motor during the first 4.00 revolutions? Express your answer in joules.

Answer 1

Part A

torque = moment of inertia * angular acceleration

so,

angular acceleration = torque / moment of inertia

angular acceleration = 2000 / 580

angular acceleration = 3.4482 rad/sec²

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Part B

4 revolutions mean = 4 * 2 = 8 rad

so,

w = sqrt ( 2a)

w = sqrt ( 2 * 3.4482 * 8)

w = 13.165 rad/sec

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Part C

work done = change in rotational kinetic energy

work done = 1/2 * I * w²

work done = 1/2 * 580 * 13.165²

work done = 50264.4 J