# What do we mean by "kinematics," "dynamics," and "mechanics?"

What do we mean by "kinematics," "dynamics," and "mechanics?"

Newton’s law of gravity and three laws of motion describe all gravitational phenomena in the universe within the range of parameters where the size of the system is smaller than hundreds of millions of light-years but bigger than the size of an atom, and is less massive than galaxy clusters but more massive than an individual atom, and which travels at a speed much slower than the speed of light. Within this range it is forces which alter an object’s otherwise uniform motion (also called inertial

motion) and the forces acting on an object determine what its new motion will look like. Most Greek philosophers believed that uniform motion refers to something that sits still and doesn’t move at all. It was Galileo who first correctly articulated what uniform motion is: uniform motion means that the object is moving at a constant velocity. This just means that its speed stays the same and its direction doesn’t change either. This notion of uniform motion isn’t limited to a boulder that doesn’t move—although this is indeed an example of an object having constant velocity since its speed (which is zero) stays the same and of course its direction isn’t changing. This notion would also apply to a very small stone in empty space (far away from any planets or stars) moving at hundreds of kilometers per hour; its speed will stay the same and its direction won’t change either so that stone is at rest. If an object has inertial motion it will move along a straight line through space and its speed will stay the same.

In the case of planets, our moon, and falling apples it is just one force—the force of gravity—which is responsible for altering their otherwise uniform motion and determining what their new motion will look like. If we are far away from any planets or stars in empty space, gravity’s influence becomes unimportant. If there are isolated objects in empty space then no forces are acting on them and therefore their motion is uniform. In the beginning of our studies we’ll only worry about a subset of mechanics called kinematics which is where we’ll study uniform motion and also non-uniform motion but without consideration of what caused that particular motion (which of course was forces or the absence of forces). Next we’ll study the second branch of mechanics which is called dynamics. In dynamics we’ll study what causes uniform and non-uniform motion—namely, the absence of forces acting on the object or there being forces acting on it. Finally we’ll combine the two and see that the same laws which are used to describe the cause of a particular kind of motion can also be used to determine exactly what that motion will look like. This is called mechanics: it combines the equations of dynamics and kinematics.

After that we’ll study rotational motion. In the case of translational motion it was forces which caused an object’s motion to deviate from remaining inertial; but in the case of rotational motion it is another quantity (although related to force)—called torque—which causes an object’s inertial rotational motion to no longer be inertial. Inertial rotational motion is a little different than inertial translational motion which we talked about earlier. An object has inertial rotational motion when its angular velocity stays the same; that is to say how rapidly a ball is spinning stays the same and the direction it is spinning in doesn’t change (for example it spins clockwise and stays that way). Taking a similar approach to our study of translational motion we’ll start out by studying inertial and non-inertial rotational motion without thinking about the cause (this is called rotational kinematics); then we’ll study what causes inertial and non-inertial rotational motion (it is torques or the absence of torques); finally we’ll use the same laws that we used to describe the cause of inertial or non-inertial rotational motion to also work out exactly what that rotational motion will look like—this is called rotational mechanics.

We will see that there is another force besides gravity; this is called the electromagnetic force. Since it is still a force it will also cause object’s to lose their inertial motion. Contact forces are when two or more enormous clumps of atoms press against each other—for example, when you push your hand against a wall. All contact forces are due entirely to electromagnetic forces. When the clumps of atoms composing your hand “press” against a wall, the atoms in your hand and the atoms in the wall become very close to one another and repel each other with electromagnetic forces. We will also investigate how electromagnetic forces effect inertial motion. But eventually we’ll ask the next question: what causes force? In the case of the force of gravity, within the range of parameters I mentioned earlier, it is a property called mass—which all matter has—which “causes” the force of gravity to manifest itself. However, when we extend the range of parameters to include sizes larger than hundreds of millions of light-years and masses greater than galaxy clusters we’ll see that the quantity which is responsible for “causing” gravity is something called energy. Fascinatingly, mass is just a form of energy; it is a particular manifestation of a much more general thing. We will also see that perhaps gravitational force (which according to General Relativity is “weakly curved” spacetime) is a particular manifestation of something much more general: the curvature of spacetime.