Angular momentum: disk with point mass on the edge

In summary, the conversation discusses a problem involving a rotating disk with an added point mass on the edge. The goal is to determine the instantaneous angular momentum and moment exerted on the disk center. There is a question about whether the total angular momentum is equal to the sum of the point mass and disk angular momenta, and whether the moments of inertia can be considered unchanged with the added point mass. The experts clarify that the total angular momentum is the sum of the constituents, but the moment of inertia is more complex due to the shifting center of mass caused by the added point mass. They also mention that the total moment of inertia is the sum of the disk's moment of inertia and the mr^2 from the point mass.
  • #1
willywilly
3
0
Hi all,

I'm treating a problem concerning a disk containing an additional point mass on the edge. The disk is moving (rotating and translating) relative to another fixed point, meanwhile it's spinning about its axes of symmetry.
I'd like to determine the instantaneous angular momentum about the disk center and the resulting instantaneous moment the system (point mass+disk) exerts on the disk center.

Is the total angular momentum equal to the angular momentum of the point mass + the angular momentum of the disk?
Is it allowed to consider the moments of inertia about the disk center unchanged when an additional point mass is added, neglecting the latter?

Thanks in advance.

Regards,
WillyWilly
 
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  • #2
you can assume the conservation of angular momentum

Not clear where the point of rotation is - is it fixed at the centre of the disk?

In other words a shift in centre of gravity when the point mass is added on the disk
 
  • #3
The rotation is about the center of gravity of the disk, called G, containing no point mass.
 
  • #4
Total angular momentum is indeed a simple sum of angular momenta of the constituents, as are the moments of inertia, but it is not that simple in your case because the moment of inertia of the disk (without considering the point mass) is different about different axes, and the presence of the point mass fixed to the disk has shiften the centre of mass outwards from the centre.edit- oh I misread, if the disk is still spinning about its centre, then the total moment of inertial is that of the disk plus the mr^2 from the point.
 
  • #5
,

Hello WillyWilly,

Great question! The total angular momentum of a system is indeed equal to the sum of the individual angular momenta of its components. In this case, the total angular momentum would be equal to the angular momentum of the point mass plus the angular momentum of the disk. This is because angular momentum is a vector quantity, meaning it takes into account both the magnitude and direction of the rotation.

As for the moments of inertia, it is possible to neglect the additional point mass when calculating the moment of inertia about the disk center. This is because the moment of inertia is a property of the object itself, and adding a point mass on the edge would not change the distribution of mass within the disk. However, it is important to note that neglecting the point mass may affect the overall dynamics of the system, so it should be taken into consideration in the overall analysis.

I hope this helps clarify your doubts. Good luck with your research!

Best regards,
 

1. What is angular momentum?

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

2. How is angular momentum calculated?

Angular momentum is calculated by multiplying an object's moment of inertia (a measure of how difficult it is to change an object's rotational motion) by its angular velocity (the rate at which the object is rotating).

3. How does angular momentum apply to a disk with a point mass on the edge?

In this scenario, the angular momentum of the disk and the point mass can be calculated separately and then added together. The disk's angular momentum is calculated using its moment of inertia and angular velocity, while the point mass's angular momentum is calculated using its mass, distance from the center of rotation, and angular velocity.

4. What happens to angular momentum when a force is applied to the disk?

According to the law of conservation of angular momentum, the total angular momentum of a system remains constant unless an external torque is applied. Therefore, if a force is applied to the disk, its angular momentum will change in response to the applied torque.

5. How is angular momentum related to rotational kinetic energy?

Angular momentum and rotational kinetic energy are related through the moment of inertia. As an object's moment of inertia increases, its angular momentum and rotational kinetic energy also increase. This means that objects with larger moments of inertia will require more energy to rotate at a given angular velocity.

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