Game Development Reference

In-Depth Information

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