Vector Angular Momentum

When the young lady to the left starts walking counter-clockwise an a platform that is able to rotate without friction, the platform will rotate clockwise. 

Momentum must be conserved.  The young lady's momentum is upward and the platform's momentum is downward.  The total momentum is zero because there is no external torque because there is no friction between the platform and the ground.  Remember to use the Right Hand Rule to determine the direction of the momentum.

We will now look at an example with external torque.

The spinning wheel above has momentum to the right,  Right Hand Rule.  When a force is applied to the axle, the torque on the system is toward you in the X axis,  Right Hand Rule.  The change in momentum must also be in the X axis as shown above.  The new momentum is the vector addition of the two momentums.  The wheel moves to the side instead of up.