Q:     What is torque?

A:     Torque is a physical  vector quantity characteristic for an object in rotational motion around a certain given axis.  By definition torque () is the cross product between the vector of position (r) of the point where a force is applied ( from an origin considered to be on the axis of rotation) and the applied force (F)  ( = r x F).   According to the definition of the cross (or vector) product, the magnitude of the torque is equal to the magnitude of r times the magnitude of F multiplied by sine of the angle () between r and F ( = r F sin ).  In this expression for magnitude of the torque, the product (r sin ) is equal to the magnitude of the distance (d) between the axis of rotation and the "line of action" of the force (F) (r sin = d).  This distance (d) is called "arm of the force."  Now, the torque can be expressed as = Fd (torque is equal to force multiplied by the arm of the force.)  Intuitively, torque can be interpreted as "force with a twist" since it results in rotation of the object on which the force is applied.

Q:     An electric motor runs at 1000 rpm and delivers 3.0 hp.  How much torque does it deliver?

A:     To solve this problem we need to convert to SI units.
P =        so        =  P/
Angular velocity () = 1000 rpm = 1000 rev/min * 1 min/60 sec
                               = 16.67 rev/sec * 2 rad/rev =  104.72 rad/sec
Power (P) = 3.0 hp = 3.0 hp * 745.70 Watt/hp = 2237.1 Watt

=  P/ =  (2237.1 Watt) / (104.71 rad/sec) = (2237.1 N m/sec) / (104.71 rad/sec)  = 21.36 N m