Average Angular Acceleration of a CD

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The average angular acceleration of a CD is calculated using the change in angular velocity over time. The initial angular velocity is converted from 460 rpm to approximately 48.17 rad/s, while the final velocity is converted from 202 rpm to about 21.15 rad/s. The total time for the CD's rotation is 3588 seconds. The calculated angular acceleration is -0.00753 rad/s², but the answer may not be accepted due to formatting issues in online grading systems like WileyPlus, which often require scientific notation. Proper formatting is crucial for successful submission in these systems.
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Homework Statement



A CD has a playing time of 59.8 minutes. When the music starts, the CD is rotating at an angular speed of 460 revolutions per minute (rpm). At the end of the music, the CD is rotating at 202 rpm. Find the magnitude of the average angular acceleration of the CD. Express your answer in rad/s^2.

Homework Equations



angular acceleration = change in angular velocity / change in time

The Attempt at a Solution



initial angular velocity in rad/s:
460rpm / 60 * 2 * Pi = 48.17rad/s

final angular velocity in rad/s:
202rpm / 60 * 2 * Pi = 21.15rad/s

time in s:
59.8min * 60 = 3588s

angular acceleration:
(21.15 - 48.17) / 3588 = -.00753rad/s^2

I'm really not sure why this is incorrect. I feel like I'm making a really obvious/face-palm type mistake.
 
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I agree with your answer.

It sounds like you are submitting this for online grading. For some reason these are known to have bugs in terms of accepting answers that are slightly off or in a different format from what the accepted answer is. I am always puzzled as to why they can't get it to act right.
 
You're exactly right. I'm using the WileyPlus system and it expected scientific notation without explicitly stating so.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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