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M z = x F y - y F x
Consider the rigid body shown in Figure 3-4 acted upon by the force F at a point away
from the body's center of mass.
Figure 3-4. Torque example
In this example F , a , and b are given and are as follows:
F = (−90 lbs) i + (156 lbs) j + (0) k
a = 0.66 ft
b = 0.525 ft
Calculate the torque about the body's center of mass due to the force F .
The first step is to put together the distance vector from the point of application of F to
the body's center of mass. Since the local coordinates a and b are given, r is simply:
r = (0.66 ft) i + (0.525 ft) j + (0) k
Now using the formula M = r × F (or the formulas for the components of the torque
vector shown earlier), you can write:
M = [(0.66 ft) i + (0.525 ft) j + (0) k ] × [(−90 lbs) i + (156 lbs) j
+ (0) k ]
M = [(0.66 ft) (156 lbs) - (0.525 ft) (−90 lbs)] k
M = (150.2 ft-lbs) k
 
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