Angular momentum of turntable problem

In summary, the conversation discusses a problem involving a rotating turntable and two falling blocks. The goal is to find the angular velocity of the turntable after the blocks hit and stick to it. The solution involves considering the moment of inertia for a disk rotating about its center and adding the moments of inertia for the two additional masses at the rim of the disk. By using this approach, the correct answer of 100 rpm is obtained.
  • #1
Vagabond7
50
11

Homework Statement



A 1.9kg , 20 cm-diameter turntable rotates at 150rpm on frictionless bearings. Two 480g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick.

what is the objects angular velocity in rpm right after this event?

Homework Equations



L=Iω where L is angular momentum, I is the moment of inertia and ω is the angular velocity
moment of inertia for a disk rotating about it's center 1/2*m*r^2

The Attempt at a Solution



Ok, so it seems like a simple conservation problem, so I tried to solve it like one.

I final*ω final = I initial * ω initial
ergo
ω final = (I initial * ω initial)/ I final

convert 150 rpm in rad/s, (150/60)*2[itex]\pi[/itex] =15.71

since the formula for the moment of inertia "I" for a disk rotating about the center is 1/2*m*r^2
I just plug in the values

(.5*1.9kg*.1^2m*15.71 rad/s)/ (.5*(1.9+.96kg)*.1^2m) = 10.44 rad/s

converting back to rpm (10.44/ 2[itex]\pi[/itex] )*60 = 99.66 rpm rounded to 100 rpm.

But this solution is incorrect. What have I done wrong?
 
Last edited:
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  • #2
You seem to believe that the final moment of inertia is that of a more massive disk, but that is not write. You should treat the system as a disk with two additional masses at its rim.
 
  • #3
I see what you're saying, but I have no idea how to account for that in the math. Another hint please?
 
  • #4
Do you know the moment of inertia for a point-mass at a radius r? Just use this (for both masses).
 
  • #5
You can consider the disk and the masses separately, and sum their ang. mom.
 
  • #6
Thank you much guys, those tips got me to where I needed to go!

Edit: Oh yeah, I made "I final" equal the sum of the moments of inertia of the disk, and the two point masses. Thanks a bunch.
 
Last edited:

1. What is angular momentum?

Angular momentum is a measure of the amount of rotational motion an object has. It is the product of an object's moment of inertia and its angular velocity.

2. How is angular momentum related to a turntable?

In the context of a turntable, angular momentum is the amount of rotational motion that the turntable has. It is affected by the moment of inertia of the turntable, which is determined by the distribution of its mass, and its angular velocity, which is the speed at which it rotates.

3. How does the angular momentum of a turntable change with different speeds?

The angular momentum of a turntable increases as its rotational speed increases. This is because the angular velocity is a factor in the calculation of angular momentum.

4. How does the angular momentum of a turntable change when the mass distribution is altered?

The moment of inertia, and therefore the angular momentum, of a turntable changes when the mass distribution is altered. For example, if more weight is added to the outer edge of the turntable, the moment of inertia increases and so does the angular momentum.

5. Why is the angular momentum of a turntable important?

The angular momentum of a turntable is important because it affects the stability and balance of the turntable. It also plays a role in the sound quality produced by the turntable, as it can impact the accuracy and consistency of the rotation.

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