Rotation around a fixed axis the same mass and velocity of rotation. Like linear momentum, angular momentum is vector quantity, and its conservation implies that the direction of the spin axis tends to remain unchanged. For this reason, the spinning top remains upright whereas a stationary one falls over immediately. The angular momentum equation can be used to relate the moment of the resultant force on a body about an axis (sometimes called torque), and the rate of rotation about that axis. Torque and angular momentum are related according to just as F = "d"p/"dt" in linear dynamics. In the absence of an external torque,
Angular velocity its dual to get a 3 dimensional pseudovector that is precisely the previous angular velocity vector formula_107: Substituting "ω" for "W" into the above velocity expression, and replacing matrix multiplication by an equivalent cross product: It can be seen that the velocity of a point in a rigid body can be divided into two terms – the velocity of a reference point fixed in the rigid body plus the cross product term involving the angular velocity of the particle with respect to the reference point. This angular velocity is the "spin" angular velocity of the rigid body as opposed to