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 origin: The relation between this linear map and the angular velocity pseudovector formula_74 is the following. Because "W" is the derivative of an orthogonal transformation, the bilinear form is skew-symmetric. Thus we can apply the fact of exterior algebra that there is a unique linear form formula_76 on formula_77 that where formula_79 is the exterior product of formula_80 and formula_81. Taking the sharp "L" of "L" we get Introducing formula_83, as the Hodge dual of "L", and applying the definition of the Hodge dual twice supposing that the preferred unit 3-vector is formula_84 where by definition. Because formula_81 is an