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Angular momentum of a rotating body is conserved in the absence of a net torque on the body. Torque is a vector, so rotational analogs of dual concepts like vectors and their products must be carefully defined. For a rotating body, the total torque on the body can be defined as the vector sum of the net torque around the body's axis of rotation and the net torque around the body, the latter being defined as the torque around any plane not corresponding to the body's axis of rotation (for example, the torque around the center of mass). The total torque on an irrotational body of mass M and radius R, rotating around an axis at an angle θ to the horizontal axis, is always 0.
The conservation of angular momentum has important implications for the motion of all rotating systems. When an object in a rotating system is acted on by an external force F, the object will not necessarily lose momentum. If F is due only to gravity (and if the object is a rigid body), then the net change in momentum is:
In the absence of friction and external forces or torques, the motion of a rigid body always looks the same in every direction except for a rotation and an acceleration. It is an exercise in the kinematics of rigid body motion to make intuitive sense of this statement. d2c66b5586
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