Free For the Love of Physics by Walter Lewin

We expect them to come to a stop at some point. No golfer could have come up with the law of inertia, since so few putts go in a straight line and so many stop wellshort of the hole. What was and still is intuitive is the contrary idea—that things naturally tend toward rest—which is why it had dominated Western thinking about these matters for thousands of years until Newton’s breakthrough.
    Newton turned our understanding of the motion of objects on its head, explaining that the reason a golf ball often stops short of the hole is that the force of friction is slowing it down, and the reason the Moon doesn’t shoot off into space, but keeps circling Earth, is that the force of gravitational attraction is holding it in orbit.
    To appreciate the reality of inertia more intuitively, think about how difficult it can be when you are ice skating to make the turn at the end of the rink—your body wants to keep going straight and you have to learn just how much force to apply to your skates at just the right angle to move yourself off of that course without flailing wildly or crashing into the wall. Or if you are a skier, think of how difficult it can be to change course quickly to avoid another skier hurtling into your path. The reason we notice inertia so much more in these cases than we generally do is that in both cases there is so little friction acting to slow us down and help us change our motion. Just imagine if putting greens were made of ice; then you would become acutely aware of just how much the golf ball wants to keep going and going.
    Consider just how revolutionary an insight this was. Not only did it overturn all previous understanding; it pointed the way to the discovery of a host of forces that are acting on us all the time but are invisible—like friction, gravity, and the magnetic and electric forces. So important was his contribution that in physics the unit of force is called a newton. But not only did Newton allow us to “see” these hidden forces; he also showed us how to measure them.
    With the second law he provided a remarkably simple but powerful guide for calculating forces. Considered by some the most important equation in all of physics, the second law is the famous F = ma. In words: the net force, F , on an object is the mass of the object, m , multiplied by the net acceleration, a , of the object.
    To see just one way in which this formula is so useful in our daily lives, take the case of an X-ray machine. Figuring out how to produce just the right range of energies for the X-rays is crucial. Here’s how Newton’s equation lets us do just that.
    One of the major findings in physics—which we’ll explore more later—is that a charged particle (say an electron or proton or ion) will experience a force when it is placed in an electric field. If we know the charge of the particle and the strength of the electric field, we can calculate the electric force acting on that particle. However, once we do know the force, using Newton’s second law we can calculate the acceleration of the particle. *
    In an X-ray machine electrons are accelerated before they strike a target inside the X-ray tube. The speed with which the electrons hit the target determines the energy range of the X-rays that are then produced. By changing the strength of the electric field, we can change the acceleration of the electrons. Thus the speed with which the electrons hit the target can be controlled to select the desired energy range of the X-rays.
    In order to facilitate making such calculations, physicists use as a unit of force, the newton—1 newton is the force that accelerates a mass of 1 kilogram at 1 meter per second per second. Why do we say “per second per second”? Because with acceleration, the velocity is constantly changing; so, in other words, it doesn’t stop after the first second. If the acceleration is constant, the velocity is changing by the same amount every second.
    To see this more clearly,