Vector Nature of Angular Quantities

      
In translational motion  F = ma and  F = /\p//\t  are vector quantities.

                                                       /\L        /\ ( I )
In angular motion   = I =  -------  =  -----------  are also vector quantities.
                                                       /\t              /\t

The liner velocities of the particles in the wheel to the left point in all different directions.  The only unique direction in space associated with the rotation is along the axis which is perpendicular to the motion. 

We use the right-hand rule to assign a direction to the vector.  If the fingers point in the direction of the motion of the particles, the thumb points in the direction of the vector of .  If the particles moved in a clockwise direction, the vector would point down.

For the drawing above,   is up if is increasing and down if is decreasing.  These are also reversed if the rotation is clockwise instead of counter-clockwise.

Since torque is due to applied force, which is a vector, the direction of the torque must be due to the direction of the applied force. 

Using another right hand rule, the right arm is aligned in the direction of the radius pointing to the point where the force is applied.  The fingers are turned in the direction of the applied force.  The thumb will point in the direction of the torque.

Observe in the drawing to the left, that the torque is pointing up.