Game Development Reference
gravitational field of another object. Thinking in terms of force fields can help you grasp
the fact that an object can exert a force on another object without having to physically
Within these two broad categories of forces, there are specific types of forces related to
various physical phenomena—forces due to friction, buoyancy, and pressure, among
others. We'll discuss idealizations of several of these types of forces in this chapter. Later
in this topic, we'll revisit these forces from a more practical point of view.
Before going further, we need to explain the implications of Newton's third law as in‐
troduced in Chapter 1 . Remember, Newton's third law states that for every force acting
on a body, there is an equal and opposite reacting force. This means that forces must
exist in pairs—a single force can't exist by itself.
Consider the gravitational attraction between the earth and yourself. The earth is ex‐
erting a force—your weight—on you, accelerating you toward its center. Likewise, you
are exerting a force on the earth, accelerating it toward you. The huge difference between
your mass and the earth's makes the acceleration of the earth in this case so small that
it's negligible. Earlier we said you are exerting a force on this topic to hold it up; likewise,
this topic is exerting a force on your hands equal in magnitude but opposite in direction
to the force you are exerting on it. You feel this reaction force as the topic's weight.
This phenomenon of action-reaction is the basis for rocket propulsion. A rocket engine
exerts force on the fuel molecules that are accelerated out of the engine exhaust nozzle.
The force required to accelerate these molecules is exerted back against the rocket as a
reaction force called thrust . Throughout the remainder of this topic, you'll see many
other examples of action-reaction, which is an important phenomenon in rigid-body
dynamics. It is especially important when we are dealing with collisions and objects in
contact, as you'll see later.
The best example of a force field or force at a distance is the gravitational attraction
between objects. Newton's law of gravitation states that the force of attraction between
two masses is directly proportional to the product of the masses and inversely propor‐
tional to the square of the distances separating the centers of each mass. Further, this
law states that the line of action of the force of attraction is along the line that connects
the centers of the two masses. This is written as follows:
F a = (G m 1 m 2 ) / r 2
where G is the gravitational constant, Newton's so-called universal constant . G was first
measured experimentally by Sir Henry Cavendish in 1798 and equals 6.673×10 −11 (N-
m 2 )/kg 2 in metric units or 3.436×10 −8 ft 4 /(lb-s 4 ) in English units.