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,
Angular velocity which shows a connection with the Lie group of rotations. We prove that angular velocity tensor is skew symmetric, i.e. formula_63 satisfies formula_64. A rotation matrix "A" is orthogonal, inverse to its transpose, so we have formula_65. For formula_66 a frame matrix, taking the time derivative of the equation gives: Applying the formula formula_68, Thus, "W" is the negative of its transpose, which implies it is skew symmetric. At any instant formula_70, the angular velocity tensor represents a linear map between the position vector formula_71 and the velocity vectors formula_72 of a point on a rigid body rotating around the