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

[Nick tringali]

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

 

[Nick tringali]

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

 

[hmmm27]

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)

 

[Nick tringali]

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.

 

[hmmm27]

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.

 

[haruspex]

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.

 

[Nick tringali]

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

 

[hmmm27]

What I’m not understanding is how they are both wrong when both equations come straight out of my reference table for angular Kinematics

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.

 

[haruspex]

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.