Why Didn't Taking the Second Derivative Solve the Angular Acceleration Problem?

AI Thread Summary
Taking the second derivative to find angular acceleration may not yield the correct answer if only tangential acceleration is considered. The total linear acceleration includes both tangential and centripetal components, which must be accounted for. The discussion highlights the importance of recognizing that total linear acceleration is a vector sum of these two components. Clarification on the formula for centripetal acceleration is also provided. Understanding these concepts is crucial for solving angular acceleration problems accurately.
Garen
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Homework Statement


35klkrc.jpg




The Attempt at a Solution


I thought I could take the second derivative and get the angular acceleration from which I could use
16b8cfa99b346f088634c4ef6c1150d0.png
where ω is the angular velocity,
023d6d214986966742c67e809c7ee176.png
is the linear tangential acceleration, and r is the radius of curvature. But for some reason, it didn't give me the right answer, anyone know where I went wrong?
 
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Hi Garen,

Garen said:

Homework Statement


35klkrc.jpg




The Attempt at a Solution


I thought I could take the second derivative and get the angular acceleration from which I could use
16b8cfa99b346f088634c4ef6c1150d0.png
where ω is the angular velocity,
023d6d214986966742c67e809c7ee176.png
is the linear tangential acceleration, and r is the radius of curvature. But for some reason, it didn't give me the right answer, anyone know where I went wrong?

Are you saying that you put in the tangential acceleration as your answer? If so, remember that they are asking for the total linear acceleration, and there is more to the total acceleration than just the tangential part.
 
aaaah thank you so much. i was totally stalking this post and you replied to it in a MOMENT OF PARADISE!
 
alphysicist said:
Hi Garen,



Are you saying that you put in the tangential acceleration as your answer? If so, remember that they are asking for the total linear acceleration, and there is more to the total acceleration than just the tangential part.

Oh, I thought that total linear acceleration was only the tangential acceleration...Would I have to include centripetal acceleration? If so, how?
 
Garen said:
Oh, I thought that total linear acceleration was only the tangential acceleration...Would I have to include centripetal acceleration? If so, how?

What is the formula for centripetal acceleration? (And remember that you have already found the angular velocity!)

Once you have found both components (the tangential and centripetal), the total is just the vector sum.
 
alphysicist said:
What is the formula for centripetal acceleration? (And remember that you have already found the angular velocity!)

Once you have found both components (the tangential and centripetal), the total is just the vector sum.

I got it! Thanks a lot for your help.
 
Garen said:
I got it! Thanks a lot for your help.

Sure, glad to help!
 

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