A wheel rotates so that the angle of rotation is proportional to the square of time. The first revolution was performed by the wheel for 8 sec. Find the angular velocity 32 sec after the wheel started.

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Solution

As the wheel rotates one time, it rotates an angle of 2 π radians. Use the following equation to determine the angular acceleration.

θ = ωi * t + ½ * α * t^2, ωi = 0
2 π = ½ * α * 8^2
32 * α = 2 π
α = 0.0625 * π

This is approximately 0.2 rad/s^2. Use the following equation to determine the angular velocity at 32 seconds.

ωf = ωi + α * t, ωi = 0
ωf = 0.0625 * π * 32 = 2 π rad/s
This is approximately 6.28 rad/s.

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