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A rotating wheel requires 5.00 s to rotate 29.0 revolutions. Its angular velocity at the end of the 5.00-s interval is 96.0 rad/s. What is the constant angular acceleration (in rad/s) of the wheel?

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MathPhys

Answer:

23.8 rad/s²

Explanation:

Using constant acceleration kinematics, we can write an equation relating the angular displacement, final angular velocity, angular acceleration, and time.

Given:

Δθ = 29.0 rev × (2π rad/rev) = 182.2 rad

ω = 96.0 rad/s

t = 5.00 s

Find: α

Δθ = ωt − ½ αt²

182.2 = (96.0) (5.00) − ½ α (5.00)²

α = 23.8 rad/s²

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