Explain how angular momentum can be expressed as the vector product of two vectors. How is its direction determined?

Angular momentum, being a vector, describes the rotational motion of a body. The expression for angular momentum can be given through the vector product between the position vector and the linear momentum vector. It therefore characterizes an object’s position relative to a specified point of rotation while the linear momentum vector further characterizes the motion of the object based on its mass and velocity.

When these two vectors are cross multiplied, the resulting angular momentum vector encapsulates the magnitude and direction of the rotational motion. The magnitude of the angular momentum will reflect the distance of the object from the axis of rotation and its velocity. This way, it will illustrate how these factors contribute to the rotational effect of the object.

The direction of the angular momentum vector is found using the right-hand rule. This rule is to be applied in the following: One points fingers of their right hand in the direction of the position vector. Then curls their fingers toward the direction of the linear momentum vector. The thumb will then point in the direction of the angular momentum vector. This directional aspect is important because it gives the axis of rotation and the sense of the angular motion, so one can get a complete understanding of the dynamics of rotating systems.

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