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the angular velocity at the start of the interval

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A variable torque is applied to a rotating wheel at t = 0 and causes the clockwise angular acceleration (alpha) to increase linearly with the clockwise angular displacement (theta) of the wheel during the next 30 revolutions.

when theta is 0, alpha is 10 rads/sec^2.
when theta is 30 revs, alpha is 20 rds/sec^2, and the angular velocity is 90 rads/sec.

What was the angular velocity at the start of the interval ( when t = 0)?

Please show all work.

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This solution shows how to calculate the angular velocity just at the instant when a variable torque is applied to a rotating wheel. The solution is detailed and well organized. The response received a '5/5' rating from the student who originally posted the question.

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