HW question w/ rotational kinetic energy

[Tony the Tutor14]

Homework Statement

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A stationary horizontal platform is free to rotate about its vertical axis. The radius of the platform is R=1.6m and its moment of inertia is 660 kgm^2. A 43 kg boy jumps on the rim of the platform with the velocity 2.2 m/s tangential to the rim. What will be the angular speed of the platform with the boy?

Homework Equations

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K(rot) = (1/2)Iw^2,
v=wr, I=mr^2

The Attempt at a Solution

: [/B]
I have been the solution of w=.197 rad/s.

I can’t figure out how to get the correct answer. I’m starting to wonder if the solution I’ve been given is incorrect. Any help would be appreciated. Thanks!

 

[Orodruin]

Please show your work (this is required according to forum rules). How have you tried to solve the problem?

 

[Tony the Tutor14]

Please show your work (this is required according to forum rules). How have you tried to solve the problem?

Sorry. This is my first post. I’ve tried a few different ways to solve it.

Set KE of the boy = KE of the disk and solve for w.

I calculated the mass of the disk for use in the KE equation.

None of these have worked.

 

[haruspex]

Sorry. This is my first post. I’ve tried a few different ways to solve it.

Set KE of the boy = KE of the disk and solve for w.

I calculated the mass of the disk for use in the KE equation.

None of these have worked.

You should only apply conservation of work when there is good reason to suppose it is conserved. In this question, there is good reason to suppose it is not. What other conservation law(s) might apply?

 

[Orodruin]

In this question, there is good reason to suppose it is not.

I would just add that it is a good exercise to think about why there is good reason to suppose that kinetic energy is not conserved. It helps to think about what happens in the case of two freely moving masses that collide and stick together.

 

[Tony the Tutor14]

I would just add that it is a good exercise to think about why there is good reason to suppose that kinetic energy is not conserved. It helps to think about what happens in the case of two freely moving masses that collide and stick together.

How about the conservation of angular momentum?

 

[haruspex]

How about the conservation of angular momentum?

Could be. In what circumstances can you apply that? Do those circumstances occur here?

 

[Tony the Tutor14]

Could be. In what circumstances can you apply that? Do those circumstances occur here?

I don’t know. Right now, using the formulas for conservation of momentum and energy, I don’t see a path to calculate the correct answer. Any direction you can provide me would be very helpful. Out of the 15 questions in this problem set this is the only one I have not solved.

 

[haruspex]

I don’t know

Angular momentum is (mostly) only meaningful in respect of a specified axis.
The condition for conservation of angular momentum of a system about a given axis is that no external force acting on the system has a torque about that axis.
In the present question, what axis wouldyou choose? Are there any external torques about that axis on the boy+platform system?

 

[Tony the Tutor14]

Angular momentum is (mostly) only meaningful in respect of a specified axis.
The condition for conservation of angular momentum of a system about a given axis is that no external force acting on the system has a torque about that axis.
In the present question, what axis wouldyou choose? Are there any external torques about that axis on the boy+platform system?

I would choose the axis of the platform and I believe the boy creates a torque about that axis.

 

[haruspex]

I would choose the axis of the platform and I believe the boy creates a torque about that axis.

The boy is part of the boy+platform system. The condition for applying the conservation law is that there are no external forces applying a torque about the axis.

 

[Tony the Tutor14]

The boy is part of the boy+platform system. The condition for applying the conservation law is that there are no external forces applying a torque about the axis.

Ok, so no law of conservation. Now I’m stuck on using KE to solve this problem.

 

[Tony the Tutor14]

Ok, so no law of conservation. Now I’m stuck on using KE to solve this problem.

I would appreciate some more assistance. I am not a student. I’m trying to help my son with his exam prep.

 

[gneill]

Ok, so no law of conservation. Now I’m stuck on using KE to solve this problem.

Rethink this conclusion! The boy is part of the system, so his influence is not an external one.

 

[Tony the Tutor14]

Rethink this conclusion! The boy is part of the system, so his influence is not an external one.

Rethink which conclusion?

 

[gneill]

Rethink which conclusion?

The conclusion that no conservation laws apply.

It is important, before you begin to write equations for a problem, that you first define what comprises the "system" being analyzed. In that way you can determine whether any forces that act are internal or external.

 

[haruspex]

Ok, so no law of conservation.

In case you still do not get what gneill is telling you...
We are considering the system consisting of the boy and the platform. So any forces between the boy and the platform are internal to the system. These do not affect the total angular momentum of that system. What external horizontal force(s) might act on the system?

 

[Tony the Tutor14]

In case you still do not get what gneill is telling you...
We are considering the system consisting of the boy and the platform. So any forces between the boy and the platform are internal to the system. These do not affect the total angular momentum of that system. What external horizontal force(s) might act on the system?

Gravity?

 

[haruspex]

Gravity?

I specified horizontal.
Why doesn't the platform go skidding across the ground?

 

[Tony the Tutor14]

If the system consists of the boy and the platform, then there are no external forces acting on it. Therefore,

I specified horizontal.
Why doesn't the platform go skidding across the ground?

The problem states it is free to rotate about its vertical axis. I can only assume it is fixed about that axis.

 

[haruspex]

there are no external forces acting on it.

No, there is a force.

it is fixed about that axis.

Right. It does not go skidding across the ground because that axle exerts whatever horizontal force is necessary to prevent it.
So now we have identified the only external horizontal force acting on the system, we come to the last hurdle: does it exert a torque about your chosen axis?

 

[Tony the Tutor14]

No, there is a force.

Right. It does not go skidding across the ground because that axle exerts whatever horizontal force is necessary to prevent it.
So now we have identified the only external horizontal force acting on the system, we come to the last hurdle: does it exert a torque about your chosen axis?

No, because the axle is the axis of rotation, so there is no torque from it.

 

[haruspex]

No, because the axle is the axis of rotation, so there is no torque from it.

Right, so you can take angular momentum of the system to be conserved about that axis (but no other).
So, what is the angular momentum of that system just before the boy lands on the platform?

 

[Tony the Tutor14]

Right, so you can take angular momentum of the system to be conserved about that axis (but no other).
So, what is the angular momentum of that system just before the boy lands on the platform?

Zero, because the platform isn’t moving.

 

[haruspex]

Zero, because the platform isn’t moving.

The system consists of the boy and the platform. The boy is moving.

 

[Tony the Tutor14]

I sincerely appreciate the effort you’ve put into help me, but your teaching method isn’t effective at this point. I would prefer if someone else could please help. Thank you for your time.

 

[haruspex]

I would prefer if someone else could please help.

I wouldn't rely on that happening. Please persevere. We are getting there.
What is the boy's angular momentum about the axis just before he lands on the platform?