Velocity the angular speed formula_27 and the magnitude of the displacement. such that Angular momentum in scalar form is the mass times the distance to the origin times the transverse velocity, or equivalently, the mass times the distance squared times the angular speed. The sign convention for angular momentum is the same as that for angular velocity. where The expression formula_33 is known as moment of inertia. If forces are in the radial direction only with an inverse square dependence, as in the case of a gravitational orbit, angular momentum is constant, and transverse speed is inversely proportional to the distance,
Cross product a and b provides an alternative definition of the cross product. The relation: can be compared with another relation involving the right-hand side, namely Lagrange's identity expressed as: where a and b may be "n"-dimensional vectors. This also shows that the Riemannian volume form for surfaces is exactly the surface element from vector calculus. In the case where , combining these two equations results in the expression for the magnitude of the cross product in terms of its components: The same result is found directly using the components of the cross product found from: In R, Lagrange's equation is a