The wheel of fortune is 2.6 meters in diameter. A contestant gives the wheel an initial velocity of 2 m/s. After rotating 540 degrees, the wheel comes to a stop. Calculate the angular acceleration of the wheel. Show your work.

The angular acceleration of the wheel of fortune is -0.125 radians per square second.

Explanation:

Let suppose that wheel of fortune is decelerated at constant rate, given that wheel of fortune stops after rotating 540 degrees with an initial tangential velocity of 2 meters per second, the initial angular velocity and the kinematic expression of final angular speed as a function of angular acceleration and position are, respectively:

Where:

- Initial tangential velocity, measured in meters per second.

- Radius of the wheel of fortune, measured in meters.

- Initial angular velocity, measured in radians per second.

- Final angular velocity, measured in radians per second.

- Angular acceleration, measured in radians per square second.

- Final angular position, measured in radians.

- Initial angular position, measured in radians.

Angular acceleration is now cleared in the second expression:

Given that and , the initial angular velocity is:

Now, if , and (180° = π rad), the angular acceleration of the wheel is:

The angular acceleration of the wheel of fortune is -0.125 radians per square second.

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