14.8 : 角運動量

Angular momentum describes the rotational motion of an object.

It is defined as the moment of the object's linear momentum about a specific point O.

Consider a particle following a curved path in an x-y plane.

The scalar formulation determines the magnitude of its angular momentum, where r represents the moment arm or the perpendicular distance from point O to the line of action of the linear momentum.

However, angular momentum is a vector quantity. So, using a right-hand thumb rule the direction of the angular momentum is shown to be perpendicular to the rotation plane.

Now, if a particle follows a space curve, the vector cross-product can help determine the angular momentum around a particular point.

In this vector representation, the angular momentum remains orthogonal to the plane encompassing the position vector and the linear momentum.

When calculating the cross product, the position vector and the linear momentum should be expressed using their Cartesian components. The angular momentum is then determined by evaluating the formed determinant.