In the previous
explanation of torque, we split the force F into its tangential
and radial components with respect to r. Alternatively, we can split
the moment arm r into parallel and perpendicular components with
respect to F (refer to Figure 1). Then, the magnitude of torque
is the perpendicular distance, r
, multiplied
by the magnitude of force, F. We can label the angle between F and
r as 
. Then, the perpendicular
distance would be
- r
= r sin()
= r
F
= r sin()
F
= r F sin()
Figure 1 Diagram of the perpendicular component, r
,
and parallel component, r
, of the moment
arm r with force F acting on it.