Chapter 4. Kinetics
Recall that kinetics is the study of the motion of bodies, including the forces that act on them. It’s now time that we combine the material presented in the earlier chapters—namely, kinematics and forces—to study the subject of kinetics. As in Chapter 2 on kinematics, we’ll first discuss particle kinetics and then go on to discuss rigid-body kinetics.
In kinetics, the most important equation that you must consider is Newton’s second law:
| F = ma |
When rigid bodies are involved, you must also consider that the forces acting on the body will tend to cause rotation of the body in addition to translation. The basic relationship here is:
| Mcg = I α |
where Mcg is the vector sum of all moments (torques) acting on the body, I is the body moment of inertia tensor, and α is the angular acceleration.
Collectively, these two equations are referred to as the equations of motion.
There are two types of problems that you will encounter in kinetics. One type is where you know the force(s) acting on the body, or you can estimate them, and you must solve for the resulting acceleration of the body (and subsequently its velocity and displacement). Another type is where you know the body’s acceleration, or can readily determine it using kinematics, and you must solve for the force(s) acting on the body.
This chapter will primarily discuss the first type of problem, where you know the force(s) acting on the body, which is more common to in-game physics. The second type of problem has become ...