A rotating wheel requires 8.00 s to rotate 27.0 revolutions. Its angular velocity at the end of the 8.00-s interval is 99.0 rad/s. What is the constant angular acceleration (in rad/s) of the wheel?

∝ = 28.92 rad/s²

Explanation:

Applying third equation of motion to the angular motion, we have:

2∝θ = ωf² - ωi²

where,

∝ = angular acceleration = ?

θ = angular displacement = (27 rev)(2π rad/1 rev) = 169.64 rad/s

ωf = final angular velocity = 99 rad/s

ωi = initial angular velocity = 0 rad/s

Therefore,

(2)∝(169.64 rad) = (99 rad/s)² - (0 rad/s²)

∝ = (9801 rad²/s²)/(38.8 rad)

∝ = 28.92 rad/s²

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