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A wheel on a game show is given an initial angular speed of 1.22 rad>s. It comes to rest after rotating through 0.75 of a turn.

(a) Find the average torque exerted on the wheel given that it is a disk of radius 0.71 m and mass 6.4 kg.

User Shaun Han
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Final answer:

The question is about determining the average torque exerted on a wheel of known dimensions and mass that comes to rest after spinning through a specific angle.

Step-by-step explanation:

The student is asking about the average torque exerted on a disk-shaped wheel of a game show when it slows down and stops. To calculate the torque, we need to determine the wheel's angular acceleration and use the relation τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration. Since the wheel completes 0.75 of a turn (which equals 0.75 * 2π rad) before stopping, and its initial angular speed is 1.22 rad/s, we can use the kinematic equation θ = ω₀t + 0.5αt² to solve for α, where θ is the angular displacement, ω₀ is the initial angular speed, and t is the time. Then, knowing that I for a solid disk is 0.5 * m * r² (with m as the mass and r as the radius), we can find the torque.

User Zhiltsoff Igor
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