1). The angular acceleration of the rotating wheel is .
2). The interval for which the angular speed of the rotating wheel is increasing is .
Further Explanation:
Given:
The initial angular speed of the wheel is .
The final angular speed of the wheel is .
The time taken by the wheel to accelerate is .
Concept:
<u>Part (1):
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The relation of the initial and final angular velocity along with the angular acceleration of the wheel is expressed as:
Substitute the values in the above expression.
Thus, the angular acceleration of the rotating wheel is .
<u>Part (2):
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Since the wheel is rotating with negative angular speed and finally it has got the positive angular speed. It means that first the speed of the wheel decreases and comes to zero in some time and then after that it starts increasing.
The time taken by the wheel to bring its speed to zero is:
Here, is zero as we need to find the time when it comes to zero angular speed.
Substitute the values in above expression.
So, the time taken by the wheel to reach zero speed is . So, for the remaining time, the speed of the wheel will be increasing.
The time for which the angular speed of the wheel is increasing is:
Thus, the interval for which the angular speed of the rotating wheel is increasing is .
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Answer Details:
Grade: College
Subject: Physics
Chapter: Rotational motion
Keywords:
Wheel, rotating, axis in the z-direction, increases linearly, -6.00rad/s, +8.00rad/s, counterclockwise rotation to be positive, angular acceleration, angular velocity.