Angular momentum of a particle problem

[yuki_meiseki]

Homework Statement

Two identical particles have equal but opposite momenta, p and -p, but they are not traveling along the same line show that the total angular momentum of this system does not depend on the choice of origin.

Homework Equations

L=r x p
Sum of torque = dL/dt

The Attempt at a Solution

Do not understand the problem at all.

 

[Dick]

Total angular momentum is r1xp+r2x(-p). If you change the origin, r1 changes to r1+d and r2 changes to r2+d. Conclusion?

 

[ogb p]

I can help clarify the problem for you. Angular momentum is a property of a particle that describes its rotational motion. It is defined as the cross product of the position vector (r) and the linear momentum (p) of the particle. In this problem, we have two identical particles with opposite momenta, but they are not traveling along the same line. This means that they are moving in different directions.

The total angular momentum of a system is the sum of the individual angular momenta of all the particles in the system. In this case, since the two particles have equal but opposite momenta, their individual angular momenta will cancel out, resulting in a total angular momentum of zero. This is because the cross product of a vector with its negative counterpart will always result in a vector with a magnitude of zero.

Now, the problem states that the total angular momentum of this system does not depend on the choice of origin. This means that the location from which we measure the position vector (r) does not affect the total angular momentum of the system. This can be proven mathematically by taking the derivative of the total angular momentum with respect to time (dL/dt) and showing that it is equal to zero, indicating that the total angular momentum is constant regardless of the choice of origin.

In conclusion, the total angular momentum of a system of two particles with equal but opposite momenta will always be zero, and it is independent of the choice of origin. This is because the particles' individual angular momenta cancel out, resulting in a net angular momentum of zero, and the choice of origin does not affect this cancellation.