How Do You Calculate Angular Motion for a Child on a Merry-Go-Round?

[LizAnn10]

Homework Statement

Okay so this is a multi part question. I think I am on the right track, but I am most likely wrong. Any help is good. If I know what to use for the equations I can usually solve it on my own.
The question is:
A child of mass 40kg is on a merry go round. The ride is a uniform disk of mass 150kg and radius 2m. The child is hanging onto a pole at a distance of 1m. Her father, mass 80kg pushes on the ride with a constant tangential force of 100N.
A) Determind the rotational inertia of the system (child and ride)
B) Determind the angular velocity in rpm of the child after 5s
C) The man releases the ride and it continues at a constant angular velocity. If the child moves to the ouside of the ride, 2m away from the center, what will be the new angular velocity?

Homework Equations

A) This was the easy one. I=1/2mr^2
B) I think this one is θ=(ω/2)t (its really ωfinal plus ωinitial but the initial ω would be zero, so I canceled it out.
I doesn't specify the revolutions so I assumed that it was just one. (I hope that is right) But I think that would make θ=6.283rad
C) I have no clue. I feel like it would be the same as B but distance, the only thing that changes, isn't a factor. Also it doesn't give a new time or anything.

The Attempt at a Solution

A) 360kgm^2
B) 150rad/s if I did it right.
C) No clue

 

[tms]

A) This was the easy one. I=1/2mr^2

What about the child?

B) I think this one is θ=(ω/2)t (its really ωfinal plus ωinitial but the initial ω would be zero, so I canceled it out.
I doesn't specify the revolutions so I assumed that it was just one. (I hope that is right) But I think that would make θ=6.283rad

The question asks for ω, not θ.

C) I have no clue. I feel like it would be the same as B but distance, the only thing that changes, isn't a factor. Also it doesn't give a new time or anything.

Something has definitely changed; see part A.

 

[LizAnn10]

Thanks for replying.
For A, I used the mass of the child plus the mass of the ride for m. Is that right?
For B, I just solved for ω, so it was really ω=2θ/t, so it was ω=2(6.283rad)/5s Is that right?
For C, I'm still not getting it..

 

[tms]

For A, I used the mass of the child plus the mass of the ride for m. Is that right?

No. Disks and point masses (assuming the child as one) do not have the same moment of inertia.

 

[Nickie]

As a scientist, it is important to approach problems like this by first identifying the key concepts and equations that apply. In this case, the key concepts are rotational motion and angular velocity, and the relevant equations are the moment of inertia (I=1/2mr^2) and the relationship between angular velocity (ω), time (t), and angle (θ) (θ=ωt).

For part A, you correctly used the moment of inertia equation to determine the rotational inertia of the system (child and ride). This is an important step in solving the problem.

For part B, you correctly identified the equation for finding the final angular velocity (ωfinal) using the initial angular velocity (ωinitial), time (t), and angle (θ). However, you made a mistake in your calculations. The correct equation to use is ωfinal=ωinitial+αt, where α is the angular acceleration. Since the ride is being pushed with a constant tangential force, there is a constant tangential acceleration (αt) as well. You can use the equation αt=τ/I, where τ is the torque and I is the moment of inertia, to solve for αt. Then, plug in the values for ωinitial, t, and αt into the equation ωfinal=ωinitial+αt to find the final angular velocity in radians per second. To convert to rpm, simply multiply by 60 seconds.

For part C, you are correct in thinking that the same equation (θ=ωt) can be used to solve for the new angular velocity. However, the key difference is that the distance from the center of rotation has changed, so the moment of inertia (I) will also change. You can use the equation I=mr^2, where m is the mass and r is the distance from the center, to solve for the new moment of inertia. Then, you can use the same process as in part B to find the new angular velocity.

In summary, to approach this problem as a scientist, it is important to identify the key concepts and equations, and to carefully consider the given information and how it affects the problem. It is also important to double check calculations and units to ensure accuracy in the final answer.