Finding the Angular Velocity of a Merry-Go-Round

In summary: Thank you for your help.In summary, the problem involves a person of mass 71 kg standing on a rotating merry-go-round platform of radius 3.2 m and moment of inertia 920 kg * m^2. The person walks radially to the edge of the platform while the platform rotates without friction with an angular velocity of 1.7 rad./s. The question asks to find the angular velocity when the person reaches the edge. By finding the change in moment of inertia due to the person's position change and using conservation of angular momentum, the final angular velocity is calculated to be approximately 4.30 rad./s.
  • #1
PeachBanana
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Homework Statement



A person of mass 71 kg stands at the center of a rotating merry-go-round platform of radius 3.2 m and moment of inertia 920 kg * m^2 . The platform rotates without friction with angular /velocity 1.7 rad./s. The person walks radially to the edge of the platform.

Homework Equations



ω^2 * r = α

The Attempt at a Solution



The first question I asked myself was, "How long did it take him to walk to the edge of the platform?"

I found α to be ≈ 29.59 rad./s but I'm having trouble finding an equation relating this to time. I don't know θ and don't know ω final. Is there another way I should be looking at this?
 
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  • #2
PeachBanana said:

Homework Statement



A person of mass 71 kg stands at the center of a rotating merry-go-round platform of radius 3.2 m and moment of inertia 920 kg * m^2 . The platform rotates without friction with angular /velocity 1.7 rad./s. The person walks radially to the edge of the platform.

You haven't stated here what the problem is.
 
  • #3
I guess that would be a slight problem! The question being asked:

Calculate the angular velocity when the person reaches the edge.
 
  • #4
I think if you just compute the change in moment of inertia due to having the person on the edge rather than at the centre of rotation, then you can use conservation of angular momentum to find the answer.
 
  • #5
Okay, that makes sense. I think I calculated "I" incorrectly.

I said the initial moment of inertia was 920 kg * m^2. Then I thought the final "I" value would be (I assumed this merry-go-round was a solid cylinder) 1/2 (3.2 m)^2 (71 kg) ≈ 363.5 kg * m^2.

L initial = (920 kg * m^2)(1.7 rad./s)
L initial ≈ 1564 kg * m^2/s

1564 kg * m^2/s = 363.52 m^2 * kg * ω
ω ≈ 4.30 rad./s
 
  • #6
PeachBanana said:
Okay, that makes sense. I think I calculated "I" incorrectly.

I said the initial moment of inertia was 920 kg * m^2. Then I thought the final "I" value would be (I assumed this merry-go-round was a solid cylinder) 1/2 (3.2 m)^2 (71 kg) ≈ 363.5 kg * m^2.

I'm quite puzzled by what you are attempting here. The moment of inertia of the merry-go-round itself is given in the problem. It's 920 kg m2. You do not have to compute it. So why are you trying to?

Also, if the calculation you posted was supposed to be a calculation of the moment of inertia of the merry-go-round, then why did you use the mass of the person in the calculations?

What you have to do is find the change in the moment of inertia of the overall system (merry-go-round + person) given that the person moves from the centre of rotation to the edge. For this purpose, I think you can probably treat the person as a point mass.
 
  • #7
Okay. I understand that much better. I was trying to calculate the change in the moment of inertia but went about it the completely wrong way.
 

FAQ: Finding the Angular Velocity of a Merry-Go-Round

1. How do you measure the angular velocity of a merry-go-round?

To measure the angular velocity of a merry-go-round, you will need to measure the time it takes for the merry-go-round to complete one full revolution. This can be done using a stopwatch or a timer. Then, divide the angle of rotation (in radians) by the time taken to get the angular velocity in radians per second.

2. What is the formula for calculating angular velocity?

The formula for calculating angular velocity is ω = θ/t, where ω represents the angular velocity in radians per second, θ represents the angle of rotation in radians, and t represents the time taken in seconds.

3. Can the angular velocity of a merry-go-round change?

Yes, the angular velocity of a merry-go-round can change. Factors such as the force applied to the merry-go-round, the mass of the merry-go-round, and the friction between the merry-go-round and the ground can all affect the angular velocity.

4. How does the angular velocity of a merry-go-round affect the riders?

The angular velocity of a merry-go-round can affect the riders by causing them to experience a centrifugal force, which pulls them away from the center of the merry-go-round. The faster the angular velocity, the stronger the centrifugal force, which can result in riders feeling dizzy or even falling off.

5. Is angular velocity the same as linear velocity?

No, angular velocity and linear velocity are not the same. Angular velocity refers to the rate of change of angular displacement, while linear velocity refers to the rate of change of linear displacement. Angular velocity is measured in radians per second, while linear velocity is measured in meters per second.

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