Angular Momentum: Single Particle

Every rotating object, like a spinning top, possesses an angular momentum L, which is mathematically expressed as the cross-product of the position vector and the linear momentum, which is mass times velocity.

The magnitude of angular momentum equals to mvrsinθ, and its SI units are kilogram meter square per second.

For example, consider a particle moving in the xy-plane and having a position vector r. The right-hand thumb gives the direction of angular momentum if the fingers are curled in the direction of rotation.

The time derivative of angular momentum can be expressed using the vector rule for the derivatives. The first term contains the cross-product of the velocity vector with itself and hence equals zero.

In the second term, mass times acceleration is the net force acting on the particle; recall that the cross product of r and F is torque. Thus, the rate of change of angular momentum is equal to the torque exerted by the net force acting on the particle.