On the highly-successful TV game show Wheel of Fortune, a contestant spins a large spinner wheel that determines the amount of money for which the contestant is playing. Typically, contestants spin the wheel at an initial rate of 3.3 rad/s, and the (constant) frictional force stops the wheel in about 2.7 seconds. If the frictional force produces a torque of 19.1 foot-pounds, estimate the moment of inertia of the wheel.
A) 15.6
B) 4.0
C) 0.0640
D) 7.2

Question

Quizplus · Accepted Answer

The moment of inertia (I) can be calculated using the formula τ = I * α, where τ is the torque and α is the angular deceleration. First, find α using the formula α = -ω / t, where ω is the initial angular velocity (3.3 rad/s) and t is the time (2.7 s). α = -3.3 / 2.7 = -1.22 rad/s². Then, solve for I: I = τ / α = 19.1 / 1.22 ≈ 15.6.

On the Highly-Successful TV Game Show Wheel of Fortune, a Contestant