Game Development Reference
In-Depth Information
Newton's Second Law of Motion
As we stated in the first section of this chapter, Newton's second law of motion is of
particular interest in the study of mechanics. Recall that the equation form of Newton's
second law is:
F = ma
where F is the resultant force acting on the body, m is the mass of the body, and a is the
linear acceleration of the body center of gravity.
If you rearrange this equation as follows:
F/m = a
you can see how the mass of a body acts as a measure of resistance to motion. Observe
here that as mass increases in the denominator for a constant applied force, then the
resulting acceleration of the body will decrease. You could say that the body of greater
mass offers greater resistance to motion. Similarly, as the mass decreases for a constant
applied force, then the resulting acceleration of the body will increase, and you could
say that the body of smaller mass offers lower resistance to motion.
Newton's second law also states that the resulting acceleration is in the same direction
as the resultant force on the body; thus, force and acceleration must be treated as vector
quantities. In general, there may be more than one force acting on the body at a given
time, which means that the resultant force is the vector sum of all forces acting on the
body. So, you can now write:
F = m a
where a represents the acceleration vector.
In 3D, the force and acceleration vectors will have x , y , and z components in the Cartesian
reference system. In this case, the component equations of motion are written as follows:
∑ F x = ma x
∑ F y = ma y
∑ F z = ma z
An alternative way to interpret Newton's second law is that the sum of all forces acting
on a body is equal to the rate of change of the body's momentum over time, which is
the derivative of momentum with respect to time. Momentum equals mass times ve‐
locity, and since velocity is a vector quantity, so is momentum. Thus:
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