MadSci Network: Physics

Re: Is total momentum (linear plus angular) conserved?

Date: Sat Dec 11 11:41:01 2004
Posted By: Jeff Yap, Physics Teacher
Area of science: Physics
ID: 1102627373.Ph

Hi Isaac,

Good question. This is one of the fundamental laws of physics, and my personal favorite.

Short answer: For any closed system, the total momentum is ALWAYS conserved.

Long answer: If you include everything that applies any kind of force or contact with an object, the sum of all of the momentums will be the same no matter how the objects interact with each other. For example, two hovercrafts collide with each other. Even if they go spinning off in different directions, the sum of the momentums before and the sum of the momentums afterwards will be the same. Including any rotational motion. So it makes sense that if both crafts are spinning furiously, they won't be moving (translationally) as fast as if they bounced and went zipping off in different directions without spinning. Even if they hit and stuck together and went off spinning, the sum of the momentums would be the same afterwards.

However, if there are external forces acting on the hovercrafts (for example, if one hovercraft is dragging a chain along the ground), you have to account for the force of the ground on the chain, and the chain on the hovercraft. In order to keep the sum of all of the momentums the same, you must include the chain and the ground in your calculations.

As far as calculating the direction, speed, and spin based on different collisions, there are so many variables, that it is difficult to establish set rules in real life. The easiest method for guesstimating the effects would be to use trigonometry and friction to calculate any rotational forces, use torque and angular momentum to calculate rotational motion, and then subtract that amount from the total momentum before the collision to get the final velocities. Perfectly smooth, frictionless objects undergoing instantaneous collisions while spinning will have trajectories like they are not rotating, but nothing in the real world will do that.

You can get pretty weird looking position plots if things happen a very specific way. If you spin an hockey puck while sliding it, there can be times when specific parts of the puck are not moving at all, but other parts are moving twice as fast as the center of mass of the puck.

I hope this helps. And remember: Conservation of momentum, it is not just a good idea, it is the law.

Jeff Yap
Mad Scientist

NASA - Conservation of Momentum
Eric Weisstein's World of Physics - Conservation of Momentum

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