Angular momentum and linear momentum relationship

[514void]

Is there loss of linear momentum of 2 objects in an elastic collision if the net angular momentum increases and vica versa?

[swansont]

A change in linear momentum of a system requires a net force. A change in angular momentum requires a net torque. One can change while the other is constant.

 

In an elastic collision there is no change either linear nor angular momentum.

[514void]

What happens if one of the objects gains angular momentum from the collision, like if a ball hits a rod near the end.

[swansont]

What happens if one of the objects gains angular momentum from the collision, like if a ball hits a rod near the end.

 

Then the other object will lose the same amount of angular momentum. That's what it means for the quantity to be conserved.

[514void]

Ok, seems a bit strange if the rod is hit by the ball right on the front of the ball, I would of thought it would bounce straight back from where it came from without spinning, even if it hits the rod in the middle or near the end.

[imatfaal]

Ok, seems a bit strange if the rod is hit by the ball right on the front of the ball, I would of thought it would bounce straight back from where it came from without spinning, even if it hits the rod in the middle or near the end.

 

And this is why we use maths and equations. Too many things that it is easy to get an answer intuitively actually yield an incorrect answer through the intuitive process. Who isn't fascinated first time they see a Newton's Cradle? Because it does stuff that initially our brains do not expect.

 

And if you do try the equations remember that with Angular momentum you need to pick a point and stick with it

[514void]

pick a point? for each object?

[imatfaal]

No pick a point and work out the angular momentum of all objects about that point; with no external torque that angular momentum will not change.

[514void]

O, i'm just concerned with 2 objects, so do i pick a frame where the net momentum is 0?

let us start out that both have 0 angular momentum.

So any collision of the 2 objects will mean that each will have the exact opposite angular momentum as the other?

 

(both objects have the same mass)

Edited March 7, 2014 by 514void

[J.C.MacSwell]

 

Then the other object will lose the same amount of angular momentum. That's what it means for the quantity to be conserved.

 

This is the both the key...and in 514's example potentially misleading if not understood in the right context. In every day language it makes no sense.

[swansont]

Ok, seems a bit strange if the rod is hit by the ball right on the front of the ball, I would of thought it would bounce straight back from where it came from without spinning, even if it hits the rod in the middle or near the end.

 

The ball doesn't have to spin to have angular momentum. Angular momentum is always measured with respect to an axis, and that is required is to have linear momentum that's not along that axis. A ball moving in a straight line can have angular momentum, though this is not always helpful in solving problems.

O, i'm just concerned with 2 objects, so do i pick a frame where the net momentum is 0?

let us start out that both have 0 angular momentum.

So any collision of the 2 objects will mean that each will have the exact opposite angular momentum as the other?

 

(both objects have the same mass)

 

It's often useful to use the center-of-momentum frame, but without details one can't say for sure it's the best.

 

Yes, absent any external torque on the system, any change in angular momentum of one object will result in an opposite change of the other, That they have equal masses doesn't matter; the actual rotational behavior will depend on the mass distribution rather than simply the mass, e.g. a solid disk will have a different rotational speed than a thin hoop of the same mass with the same angular momentum.

[514void]

I would of thought that an objects angular momentum would be around an axis that went through the center of mass of the object.

 

So when you say that angular momentum is conserved, you mean that both objects center of mass has angular momentum around the axis of the center of mass of both objects?

and this is conserved?

what about each objects angular momentum, is this considered in the calculation?

Edited March 7, 2014 by 514void

[imatfaal]

I would of thought that an objects angular momentum would be around an axis that went through the center of mass of the object.

...

 

That is an angular momentum - but angular momentum can be based on any axis at any point; some will give zero, and others for same system will give more than zero. Rather than guess and hope you might chance upon a correct answer why not invest some time in actual science. Read up on hyperphysics or a similar web-resource. Or if you have the time take a look at Walter Lewin's lectures on Classical Mechanics.

 

http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html

http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/

 

Far more rewarding than blindly stabbing in the dark. Remember that we see further if standing on the shoulders of giants - so take advantage of the great resources explaining millennia of science.

[swansont]

I would of thought that an objects angular momentum would be around an axis that went through the center of mass of the object.

 

 

You can choose any axis, just as you can choose any inertial frame for conservation of linear momentum. The axis of rotation of an object often makes for the easiest calculation, but it's still conserved when you choose another axis. The best method of solution is heavily context-dependent. You can't prescribe a best method without knowing the specific problem.

[studiot]

 

I would of thought that an objects angular momentum would be around an axis that went through the center of mass of the object.

 

 

In our 3D world there are actually 3 distinguishable axes.

 

There are many beautiful an interesting phenomena without trying to invent some by guesswork.

 

The equations everyone are referring to are known as Euler's Equations. These can give rise to chaotic action as can be seen and tested in this simple example.

 

Take a brick shaped object eg a book, a matchbox, a box of chocolates, or even a small brick, so that the length, breadth and depth are all different.

 

Take the block by a pair of opposite faces and and toss it up the into the air, spinning it at the same time.

 

You will find that the block spins readily and stably about two of the three axes, defined by the faces, but starts to wobble very quickly about the third.