Why is angular momentum defined with a cross product?

I first searched why is Torque defined as a cross product and a lot of people answered that it is defined as a cross product because angular momentum is defined that way and it is only logical that Torque and angular momentum have the same direction.

What is the relationship of linear momentum and radius to angular momentum?

Linear momentum (p) is defined as the mass (m) of an object multiplied by the velocity (v) of that object: p = m*v. With a bit of a simplification, angular momentum (L) is defined as the distance of the object from a rotation axis multiplied by the linear momentum: L = r*p or L = mvr.

Why is angular momentum r cross P?

In three dimensions, the angular momentum for a point particle is a pseudovector r × p, the cross product of the particle’s position vector r (relative to some origin) and its momentum vector; the latter is p = mv in Newtonian mechanics.

Is angular momentum a cross product?

The angular momentum →l of a particle is defined as the cross-product of →r and →p, and is perpendicular to the plane containing →r and →p: The angular momentum with respect to the origin is →l=→r×→p, which is in the z-direction.

What is linear momentum and angular momentum of particles?

Angular Momentum. We consider a particle of mass m, with velocity v, moving under the influence of a force F . The angular momentum about point O is defined as the “moment” of the particle’s linear momentum, L, about O. Thus, the particle’s angular momentum is given by, HO = r × mv = r × L .

How is angular momentum different from linear momentum?

Angular momentum is inertia of rotation motion. Linear momentum is inertia of translation motion. The big difference is that the type of motion which is related to each momentum is different. It is important to consider the place where the force related to rotation applies, which is appears as ‘r’ in the formula.

What is the relation between angular momentum and kinetic energy?

If angular momentum is same for two objects, kinetic energy is inversely proportional to moment of inertia. Moment of inertia of the object whose kinetic energy is lesser will have greater magnitude.