Angular Speed Problem: Understanding the Effects of Weight Release on Rotation

[kirby27]

A student is sitting on a frictionless rotating stool with her arms outstretched holding equal heavy weights in each hand. If she suddenly let's go of the weights, her angular speed will:

A) increase
B) stay the same
C) decrease

attempt: i think it's B because angular speed is V/r and does not depend on mass. is this the correct thought process?

 

[PeterO]

A student is sitting on a frictionless rotating stool with her arms outstretched holding equal heavy weights in each hand. If she suddenly let's go of the weights, her angular speed will:

A) increase
B) stay the same
C) decrease

attempt: i think it's B because angular speed is V/r and does not depend on mass. is this the correct thought process?

I believe your answer is correct. Not over keen on you reason.
This problem relates to conservation of momentum, and it trying to distract you into thinking that if momentum is conserved, and the mass is reduced [it is now just her, not her plus masses] then velocity will increase.
However here, any part of the original angular momentum the masses had will go with those masses when she "lets go of them"

 

[kirby27]

can anyone else also confirm this answer?

 

[BetoG93]

Option B is wrong, definitely.

 

[BetoG93]

The reduction of mass makes the moment of inertia smaller. If angular momentum is conserved, how do you think would angular speed change? It is easy to tell it taking in account what I said above.

 

[netgypsy]

You really need to try this if you think it makes no difference. Look at the formula definition of moment of inertia. It depends on both mass and the location of the mass. So when you toss the mass what do you change?

Than do as suggested and look at conservation of angular momentum.

 

[PeterO]

The reduction of mass makes the moment of inertia smaller. If angular momentum is conserved, how do you think would angular speed change? It is easy to tell it taking in account what I said above.

This is the sucker answer!

Yes the moment of inertia is smaller, but also the angular momentum.

To begin with, the person had a share, and the masses had a share of the original.

Since the masses were simple released, not thrown away in any particular direction, they took their share with them - leaving behind the person, with his/her original share.

This is the same example as traveling on a skate board at constant speed, carrying two 20kg masses, one in each out-stretched hand. You then release the masses.
You do not speed up! [the masses don't stop moving forwards either-until they hit the ground!]

 

[PeterO]

You really need to try this if you think it makes no difference. Look at the formula definition of moment of inertia. It depends on both mass and the location of the mass. So when you toss the mass what do you change?

Than do as suggested and look at conservation of angular momentum.

The key is that the masses are not "tossed". The masses are merely released.

Perhaps you should try this for yourself.

 

[PeterO]

can anyone else also confirm this answer?

If you wait long enough, someone who understands the situation will confirm that answer.

 

[BetoG93]

If angular momentum doesn't change, then the product of the initial angular speed and moment of inertia is equal to the product of the final angular speed and final moment of inertia.

 

[PeterO]

If angular momentum doesn't change, then the product of the initial angular speed and moment of inertia is equal to the product of the final angular speed and final moment of inertia.

You are right -- IF the angular momentum doesn't change.

But the angular momentum of the system does change, since the system separates.

The speed and angular momentum of the person does not change - meaning that part of the momentum that is "with" the person.

The momentum of the masses has gone away with the masses, and eventually been transferred to the Earth when they finally impacted.

Had the person, instead, drawn the two masses in towards the centre, they would increase the speed but they just let go!

If you have access to a child's merry-go-round in a park - go and try it.
position yourself close to the edge, so that you can hold a good solid mass out over the edge as it rotates. Release the mass - don't throw it! - and see what happens.

 

[PeterO]

If angular momentum doesn't change, then the product of the initial angular speed and moment of inertia is equal to the product of the final angular speed and final moment of inertia.

This is the rotational equivalent of the classic filling and emptying of a rail car with grain.

The rail car rolls freely under a hopper, from which pours a quantity of grain - filling the car.

The car then continues to roll, to a point where the bottom of the car opens, depositing the grain into a second hopper.

In the first part, the car slows down. The car has a certain amount of translational momentum. The falling grain has none [it is moving down, not along]. That means that as the mass increases, the car and load slow down. [actually the car slows down, the grain speeds up]

When the car is dropping its load, however, it does not speed up. All the translational momentum the grain took from the car during the loading phase, it takes with it during unloading.

Although the grain falls vertically into the cart, it falls out with some forward velocity during the unloading.

 

[JHamm]

It is definitely B, the reason you would spin faster by pulling your hands in is because the kinetic energy must be maintained, if by dropping weights you somehow sped faster then you just invented free energy.

 

[netgypsy]

Very interesting. Conservation of momentum does apply but you do have to consider the momentum of the masses when they are released as part of the system.

 

[netgypsy]

You really should try this. When the masses are pulled inward you can feel a force that results from the fact that they had a certain linear velocity and wish to maintain that so they now make more rpm's and pull you along with them. The reverse is true if you let your arms out. But releasing the masses and not moving your arms, even though you definitely have a smaller moment of inertia, the masses you are holding as you travel at constant rpm, don't cause you to gain or lose rpm's when released, BUT you would be easier to slow down now if someone grabbed you.

Great question.