Intuitive Concept of Force and Inertia

Force, in everyday language, is any push or pull that can start a body moving, stop a moving body, speed it up, slow it down, or change the direction in which it is travelling; a force can also change a body's shape (squeezing a rubber ball, stretching a spring). None of these effects needs a formal definition to be recognised -- pushing a stalled handcart, catching a fast-moving ball, or pulling open a heavy door are all familiar examples of applying a force and seeing one of these effects follow.

Sitting alongside this intuitive idea of force is the equally intuitive idea of inertia: every body has a built-in reluctance to change whatever state of motion (or of rest) it is currently in. A book lying on a table stays exactly where it is unless something pushes or pulls it; a ball rolling on a very smooth floor keeps rolling, in a straight line, at very nearly the same speed, for far longer than a ball rolling on a rough floor, because the rough floor's friction is doing more work to change the ball's state of motion. A sharp, sudden flick of a card resting under a coin, balanced on the rim of a glass, sends the card flying off sideways while the coin -- because of its own inertia -- barely has time to respond to the brief sideways force and instead drops almost straight down into the glass. Jerking a tablecloth out from under plates and cutlery arranged on top of it relies on the very same idea: the jerk lasts too short a time for friction to drag the heavier crockery along with the cloth, so the crockery's own inertia keeps it very nearly where it started.

This intuitive picture -- force as a cause of change, inertia as a body's resistance to that change -- is exactly what Sir Isaac Newton turned into three precise, quantitative laws of motion, which this chapter now builds up in order: the first law (Section 4.2), which states the idea of inertia formally; the second law (Section 4.3), which connects force quantitatively to the rate of change of momentum; and the third law (Section 4.5), which governs how two bodies act on each other. From there, the chapter develops the ideas of impulse and impulsive force, the conservation of linear momentum, the systematic free body diagram method for analysing any mechanics problem, the equilibrium of several concurrent forces acting at a single point, a detailed treatment of static, kinetic and rolling friction (including the angle of friction and the angle of repose), and finally the dynamics of uniform circular motion -- covering centripetal force, the banking of roads, and, as its own dedicated topic, the centrifugal pseudo-force felt in a rotating frame.