Angular kinematic problem -- An accelerating merry-go-round

AI Thread Summary
The discussion revolves around a kinematic problem involving a merry-go-round that accelerates to a final angular velocity of 10 revolutions per minute over 20 seconds. Participants express confusion regarding the calculation of angular displacement (theta) and why two different answers were obtained. It is suggested that the participant clarify what theta represents, as the calculations may have incorrectly used different time intervals. The discrepancy in answers arises from using time values of 2 seconds and 20 seconds, leading to vastly different results. Understanding the definitions and proper application of angular kinematics is emphasized as crucial for resolving the confusion.
Nick tringali
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Homework Statement
Hopefully I did everything up to the theta part correctly but I do not understand how I’m getting 2 different answers using 2 different equations. It’s worth noting that I designed this problem myself. Also what would be the units for theta in this case and the units for s in s= r *theta
Relevant Equations
Omega final ^2= omega initial^2 +2 alpha theta
Theta = omega initial * time + .5 alpha*time^2
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Also if you can’t read my handwriting it says a merry-go-round is rotating 10 revolutions every minute at its final angular velocity and it took 20 seconds to reach that speed
 
Nick tringali said:
a merry-go-round is rotating 10 revolutions every minute at its final angular velocity
A bit painful to follow you needlessly approximate a ##\pi## early on and end up with calculating a rev every 5.988s.

What's the actual question ? (poor eyesight and an itty-bitty laptop screen)
 
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hmmm27 said:
A bit painful to follow you needlessly approximate a ##\pi## early on and end up with calculating a rev every 5.988s.

What's the actual question ? (poor eyesight and an itty-bitty laptop screen)
The actual question is Find frequency find angular velocity find the tangent velocity find centripetal force find linear acceleration find angular acceleration and the part where I got lost is to find Theta, which I don’t really know what it is or how it’s different from s. My question about this question is why I’m getting 2 different answers for theta.
 
Nick tringali said:
the part where I got lost is to find Theta, which I don’t really know what it is or how it’s different from s. My question about this question is why I’m getting 2 different answers for theta.
Your scribbling for "bonus" seems to indicate that ##\theta## is supposed to be the angular displacement during 2 seconds at final velocity, so both answers are wrong.

I think your first step should be deciding, not the value of ##\theta##, but what ##\theta## is supposed to represent. Since you wrote the question yourself, that shouldn't be too difficult.
 
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Nick tringali said:
The actual question is Find frequency find angular velocity find the tangent velocity find centripetal force find linear acceleration find angular acceleration and the part where I got lost is to find Theta, which I don’t really know what it is or how it’s different from s. My question about this question is why I’m getting 2 different answers for theta.
In one of your methods you used t=2s instead of t=20s.
 
hmmm27 said:
Your scribbling for "bonus" seems to indicate that ##\theta## is supposed to be the angular displacement during 2 seconds at final velocity, so both answers are wrong.

I think your first step should be deciding, not the value of ##\theta##, but what ##\theta## is supposed to represent. Since you wrote the question yourself, that shouldn't be too difficult.
What I’m not understanding is how they are both wrong when both equations come straight out of my reference table for angular Kinematics
 
Nick tringali said:
What I’m not understanding is how they are both wrong when both equations come straight out of my reference table for angular Kinematics
hmmm27 said:
Your scribbling for "bonus" seems to indicate that ##\theta## is supposed to be the angular displacement during 2 seconds at final velocity, so both answers are wrong.

I think your first step should be deciding, not the value of ##\theta##, but what ##\theta## is supposed to represent. Since you wrote the question yourself, that shouldn't be too difficult.
 
hmmm27 said:
Your scribbling for "bonus" seems to indicate that θ is supposed to be the angular displacement during 2 seconds at final velocity,
As I read it, the right hand scribble gives the displacement from rest over 2 seconds at the calculated acceleration. The left hand gives it over 20 seconds, hence their ratio of 100:1.
 
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