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 3.1 rad/s, and the (constant) frictional force stops the wheel in about 2.5 seconds. If the frictional force produces a torque of 19.1 foot-pounds, estimate the moment of inertia of the wheel.
A) 15.4
B) 3.9
C) 0.0649
D) 7.1

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_final - ω_initial) / time. Since the wheel stops, ω_final = 0, and ω_initial = 3.1 rad/s. So, α = -3.1 / 2.5 = -1.24 rad/s². Then, I = τ / α = 19.1 / 1.24 ≈ 15.4.

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