# Angular Momentum

JoVE Core
Mechanical Engineering
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JoVE Core Mechanical Engineering
Angular Momentum

### Nächstes Video14.9: Relation Between Moment of a Force and Angular Momentum

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.

## Angular Momentum

Angular momentum characterizes an object's rotational motion and is defined as the moment of its linear momentum about a specified point O. When a particle moves along a curved path in the x-y plane, the scalar formulation calculates the magnitude of its angular momentum, utilizing the moment arm (d), representing the perpendicular distance from point O to the line of action of the linear momentum. Despite being scalar in formulation, angular momentum is inherently a vector quantity. Its direction is ascertained through the right-hand rule, perpendicular to the rotation plane.

If the particle traces a space curve, the vector cross-product becomes instrumental in determining the angular momentum around a specific point. In this representation, the angular momentum maintains orthogonality to the plane formed by the position vector and linear momentum. For computations involving the cross product, expressing the position vector and linear momentum in Cartesian components is crucial. The angular momentum is then established by evaluating the determinant formed by these components. This comprehensive approach ensures an accurate representation of angular momentum in both magnitude and direction for objects undergoing rotational motion.