Angular Momentum of a body after it loses mass

In summary, the conversation discussed the concept of angular momentum and whether the remaining rotating body would experience a change in angular velocity if an element detached and flew off tangentially. The conclusion was that as long as the angular momentum of the detached element remains the same, the rest of the body's angular velocity will also remain constant.
  • #1
SmoothCat
2
0
Hey guys.

If a body is spinning around the z - axis and an element of that body detaches on its own and flies off tangentially, does the rest of the remaining rotating body experience a change in angular velocity?

My thought is that the angular velocity of the remaining rotating body remains constant (same as body+elements' combined angular velocity at the start), just like velocity of a man holding a bowling ball on a moving skateboard remains constant before and after he drops it because both bodies keep the same momentum before and after the release, so its all good.

Now for the rotating issue...

The body (without the element) has a certain angular momentum as it spins. The element itself has a moment of inertia mR^2 and also has its own angular momentum, which is exactly mvR or in terms of w, mwR^2. Now, after the element flies off on a tangent, it has the same angular momentum with respect to the axis of rotation as when it was attached, no matter how far it flies right, which is ---- m(r x v), which always works out to be of magnitude mvR, which is the same as before?

So does this mean that the body (without the element) would just keep rotating at the same angular velocity that the entire body + element had at the start of the problem because the angular momentum of the element never changes, so the same would need to be true for the remaining body as well.


Please only send me a reply to this question if your willing to give me somewhat of a detailed response, because I'm really struggling with this idea...
 
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  • #2
Welcome to PF!

Hey there SmoothCat! Welcome to PF! :smile:
SmoothCat said:
If a body is spinning around the z - axis and an element of that body detaches on its own and flies off tangentially, does the rest of the remaining rotating body experience a change in angular velocity?

Please only send me a reply to this question if your willing to give me somewhat of a detailed response, because I'm really struggling with this idea...

If it flies off at the same speed as its tangential speed just before … so its angular momentum (about the centre) stays the same … then no, there's no change in angular velocity of the rest.

That's because if the angular momentum of the detached part stays the same, then so must the angular momentum of the rest. :smile:

(I'm sorry, but any more detailed response would be superfluous! :wink:)
 
  • #3
Thanks man, that answer was plenty. I just wanted to get more than a yes or no answer type thing. But, I'm glad that the answer matches what I was thinking and things didn't get messy!
 

1. What is Angular Momentum?

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

2. How does an object's angular momentum change after it loses mass?

After an object loses mass, its moment of inertia decreases, causing its angular momentum to decrease as well. This is because the object's distribution of mass has changed, affecting its rotational motion.

3. Is angular momentum conserved after an object loses mass?

Yes, according to the law of conservation of angular momentum, the total angular momentum of a system remains constant unless acted upon by an external torque. Therefore, although an object's angular momentum may decrease after losing mass, the total angular momentum of the system will remain the same.

4. How does the direction of an object's angular momentum change after it loses mass?

The direction of an object's angular momentum is determined by the direction of its angular velocity. After losing mass, an object's distribution of mass may change, causing its angular velocity to change as well. This change in direction of the angular velocity will result in a change in the direction of the object's angular momentum.

5. Can an object's angular momentum ever increase after losing mass?

No, an object's angular momentum can only decrease after losing mass. This is because the moment of inertia, which is a factor in the calculation of angular momentum, is directly proportional to an object's mass. As the mass decreases, the moment of inertia decreases, causing the angular momentum to decrease as well.

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