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A potter's wheel rotates with an angular acceleration of magnitude α = 6at3 − 5bt2, where...

A potter's wheel rotates with an angular acceleration of magnitude

α = 6at3 − 5bt2,

where t is the time in seconds, a and b are constants, and α has units of radians per second squared. The initial position of the wheel is θ0 and the initial angular speed is ω0. Obtain expressions for the angular speed and the angular displacement of the wheel as a function of time. (Assume all motion is in the same direction. Use the following as necessary: a, b, ω0, and t.)

ω(t) =
Δθ(t) =
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Angular acceleration is given by

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