Multi-angular Momenta: Q re Angular Momentum (L)

  • Thread starter RodB
  • Start date
In summary, the conversation revolves around the concept of angular momentum and its relativity to the chosen axis in the frame of reference. The bullet in discussion has a fixed linear momentum and a constant angular momentum as it travels towards the target. However, if the aim is off and the bullet misses the target, it still maintains the same linear momentum but the angular momentum becomes numerically different. This leads to the realization that the bullet can have multiple angular momenta simultaneously, each relative to a different axis in the frame. It is noted that unlike linear momentum, angular momentum is not an absolute quantity and is always relative to the chosen axis. The conversation also touches upon the difference between the moment of inertia for a rotating body and a symmetric sphere. Overall
  • #1
RodB
15
0
I have a Q re angular momentum (L) that's causing some heated discussion. A bullet is fired off center toward a rotatable target with an axis from, say, 100m (like a ballistic pendulum). The bullet has a fixed linear momentum and an L that remains constant as it travels toward the target -- Pxr stays constant as R and the angle change in sync.

Now say the shooter's aim is off and the bullet will miss the target a bit. In this case the bullet has the same constant numerical value of linear momentum (with a small change in the vector due to the aim) and a similarly constant L, but this L is numerically different from the first. This means that the bullet can have an angular momentum with a different target separated by distance and angle from the first target (but all in the same fixed unmoving coordinate system), and that this L is different numerically from the first.

The same bullet now has TWO different numerical angular momenta simultaneously. It then follows that the bullet has a simultaneous momenta with MANY (theoretically infinite) "targets". The angular momentum, in this scenario, is not a specific, single, explicit, inherent quality like linear momentum, but rather it is multiple, with each relative to some other object (axis) within the frame. Does anyone agree or disagree? (A rotating body's L is different and seems specific and inherent, but that's not the debate.)
 
Physics news on Phys.org
  • #2
RodB said:
Pxr stays constant as R and the angle change in sync.

what you want to say is that the 'moment arm' stays constant i.e. the value [itex]r\sin(\theta)[/itex] stays constant.

RodB said:
The same bullet now has TWO different numerical angular momenta simultaneously. It then follows that the bullet has a simultaneous momenta with MANY (theoretically infinite) "targets". The angular momentum, in this scenario, is not a specific, single, explicit, inherent quality like linear momentum, but rather it is multiple, with each relative to some other object (axis) within the frame. Does anyone agree or disagree? (A rotating body's L is different and seems specific and inherent, but that's not the debate.)

yes. you are right. But the way you state it is wrong. When we talk about angular momentum, or any moment, be it torque or moment of inertia, we need to specify about which axis we are calculating that moment. This is the reason the moment of Inertia for say, a cylinder is different along different axis. About a definite axis, the angular momentum is always unique and an inherent quality.

However, you would also like to note that since a sphere is symmetric about it's center, for the sphere, the moment of inertia is the same about any axis passing through the center.

Take the case of linear momentum. If an object having mass 'm' and velocity 'v' has momentum [itex]p = mv[/itex]. Now, let us say you are moving at a velocity 'v', so, for you as an observer the velocity of the object now is 0 and hence the linear momentum [itex]p = 0[/itex]. similarly, depending on the frame of your reference even the linear momentum has different values.

There is no such thing as 'absolute momentum'. It is always relative to the frame of reference you are viewing it from and for all moments, it is relative to the axis you choose.
 
  • #3
Thanks, rohanprabhu

So, in the same frame linear momentum is fixed (sans any force) and constant no mater how one looks at it. Angular momentum (again in a same frame) of any particular mass is relative to whatever axis one chooses to relate it to. It shouldn't have been that hard! Slap! Slap! As you point out (the obvious :redface: ) even singular rotating masses have different Ls depending on which axis one chooses.
 

What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of an object around an axis. It is calculated by multiplying the object's moment of inertia by its angular velocity.

How is angular momentum measured?

Angular momentum is measured in units of kilogram-meters squared per second (kg•m²/s) in the SI system. In the cgs system, it is measured in units of gram-centimeters squared per second (g•cm²/s).

What is the conservation of angular momentum?

The conservation of angular momentum states that in a closed system, the total angular momentum remains constant. This means that if there are no external torques acting on the system, the initial angular momentum will be equal to the final angular momentum.

What is the difference between orbital and spin angular momentum?

Orbital angular momentum is associated with the motion of an object around an axis, while spin angular momentum is associated with the internal rotation of an object. Orbital angular momentum is also dependent on the distance from the axis of rotation, while spin angular momentum is intrinsic to the object and does not depend on distance.

How does multi-angular momentum affect the stability of an object?

Multi-angular momentum, or the combination of both orbital and spin angular momentum, can affect the stability of an object by influencing its orientation and rotational motion. Objects with a high amount of multi-angular momentum may be more difficult to control and can exhibit complex rotational behavior.

Similar threads

Replies
23
Views
872
  • Classical Physics
Replies
10
Views
712
Replies
3
Views
1K
Replies
1
Views
291
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
821
Replies
1
Views
1K
  • Introductory Physics Homework Help
10
Replies
335
Views
7K
  • Introductory Physics Homework Help
Replies
1
Views
789
Back
Top