Force and Motion — Newton's Three Laws

1.Speed, velocity, and acceleration

Speed tells you how fast something is going: distance traveled divided by the time taken. Velocity is the same quantity with direction included. A bicycle circling a track at 30 km/h has a constant speed, but because its direction keeps changing, its velocity is constantly changing.

Acceleration tells you how quickly velocity changes. It is expressed as how many m/s the velocity changes in 1 second, so its unit is m/s² (meters per second squared). Speeding up is not the only kind of acceleration: slowing down and changing direction are also motion with acceleration.

You will often need to convert units, too. 1 km/h means covering 1000 m in 3600 seconds, so dividing a value in km/h by 3.6 gives m/s.

2.The first law: the law of inertia

If no net force (the combined total of all the forces) acts on an object, an object at rest stays at rest, and a moving object keeps moving in a straight line at the same velocity. This tendency to keep its state of motion is called inertia. The greater the mass, the greater the inertia.

When a bus suddenly pulls away, your body lurches backward because the bus moves forward while your body tends to stay where it is. When the bus brakes hard, you lurch forward, because your body tends to keep going at its original speed. A seat belt is a device that stops inertia from throwing your body forward.

The feeling that “you have to keep pushing to keep something moving” is an illusion created by friction and air resistance. When you stop pedaling a bicycle, it slows to a stop not because a force has disappeared but because friction and air resistance act in the opposite direction. On ice, where there is almost no friction, or in space, an object that has been pushed once slides for a very long time.

3.The second law: the law of acceleration, F = ma

When a net force acts on an object, the object accelerates in that direction. The acceleration is proportional to the force and inversely proportional to the mass. Push with the same force, and an empty shopping cart speeds up easily while a full one barely picks up speed.

The unit of force is the N (newton). 1 N is the force that gives an object with a mass of 1 kg an acceleration of 1 m/s². On Earth, weight is the force equal to mass times the gravitational acceleration g (about 9.8 m/s²). Mass is the same everywhere, but weight depends on where you are. On the Moon your weight drops to about one-sixth, but your mass stays the same.

4.Do heavier objects fall faster?

The idea that “heavy objects fall faster than light ones” was long treated as common sense. But if you ignore air resistance, all objects fall with the same acceleration regardless of their mass. F = ma explains why.

An object with twice the mass is pulled by Earth with twice the force (its weight, m × g), but it is also twice as hard to get moving (its inertia, or mass). So a = F ÷ m = (m × g) ÷ m = g: the mass cancels out, and the acceleration is always g (about 9.8 m/s²). The experiment on the airless surface of the Moon, in which a hammer and a feather were dropped together and hit the ground at the same time, demonstrates this.

In real air, a feather falls slowly because its air resistance is large compared with its weight. As a falling object speeds up, air resistance grows until it equals the weight, and then the object stops speeding up; the speed at that point is called terminal velocity. A parachute is a device that increases air resistance to lower terminal velocity.

5.The third law: the law of action and reaction

When object A exerts a force on object B, B simultaneously exerts a force on A that is equal in size and opposite in direction. Forces never arise alone; they always come in pairs between two objects.

When you walk, your foot pushes the ground backward and the ground pushes your foot forward, moving you ahead. A rocket pushes gas hard out the back, and the gas pushes the rocket forward. When you jump from a boat onto the shore and the boat is pushed backward, it is the same principle.

A common misconception is that “action and reaction are equal in size, so they cancel each other out.” The two forces act on different objects, so they do not cancel. When a truck and a bicycle collide, the forces they exert on each other are equal, but the acceleration (change in velocity) of the lighter bicycle is far greater, and so is the damage.

6.Friction — both a hindrance and a helper

Friction is a force between two surfaces in contact that acts in the direction that opposes motion. It is greater when the surfaces are rougher and when they are pressed together harder. Bicycle brakes slow the wheels with friction, and in the process kinetic energy turns into heat, which makes the brakes hot.

But without friction, you couldn't even walk. You need friction between the soles of your shoes and the ground in order to push the ground backward. You slip on an icy road because there is too little friction. Tire treads and anti-slip strips on stairs increase friction, while lubricating oil and bearings in machines reduce it.