Rotational Kinematics Time Problem

AI Thread Summary
The problem involves a spinning wheel with an angular acceleration of -4.40 rad/s², transitioning from an initial angular velocity to a final angular velocity of -24.0 rad/s, while experiencing zero angular displacement. To find the time required for this change in angular velocity, one can apply rotational kinematics formulas. The key equations relate angular acceleration, change in angular velocity, and time. The urgency of the request highlights the need for a prompt solution before the deadline. The discussion emphasizes the application of rotational kinematics to solve the problem efficiently.
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Homework Statement


A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -4.40 rad/s^2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -24.0 rad/s. While this change occurs, the angular displacement of the wheel is zero. (Note the similarity to that of a ball being thrown vertically upward, coming to a momentary halt, and then falling downward to its initial position.) Find the time required for the change in the angular velocity to occur.

Homework Equations


All Rotational Kinematics Formulas

The Attempt at a Solution


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Thank you in advance!
 
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Can somebody please help me? I need this answer turned in by 11:59pm tonight! D:
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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