Force and Laws of Motion

Why does a ball roll to a stop? Why are you pushed back into your seat when a car speeds up? The answers lie in force and motion. In the seventeenth century Isaac Newton summed up the whole behaviour of moving objects in just three laws. These laws of motion are among the most important and most tested ideas in all of science.

The laws need a precise language first. Motion is simply a change in position over time, described by distance, velocity and acceleration. Forces also transfer energy when they move objects, an idea captured by work, energy and power. This topic covers the full chain: describing motion, the laws that govern it, and the energy involved.

Two words that sound similar mean different things:

• Distance is the total length of the path travelled. It has only size (magnitude), making it a scalar.
• Displacement is the shortest straight-line distance from the start to the end, in a particular direction. It has both size and direction, making it a vector.

For example, if you walk around a circular track and return to the start, your distance is the full lap. Your displacement is zero. Displacement can never be greater than distance.

How fast something moves is measured in two related ways:

• Speed is the distance travelled per unit time (a scalar). Average speed = total distance ÷ total time.
• Velocity is speed in a given direction (a vector), measured as displacement per unit time.

A car going round a bend at a steady 40 km/h has constant speed but changing velocity. Its direction keeps changing, so its velocity changes too. Both are measured in metres per second (m/s).

Acceleration is the rate of change of velocity with time. It tells us how quickly an object speeds up or slows down.

• When velocity increases, acceleration is positive.
• When velocity decreases (braking), acceleration is negative, sometimes called deceleration or retardation.

An object moving at constant velocity has zero acceleration. Acceleration is measured in metres per second squared (m/s²).

For an object moving with uniform (constant) acceleration, three equations connect its quantities: initial velocity (u), final velocity (v), acceleration (a), time (t) and distance (s):

• v = u + at
• s = ut + ½at²
• v² = u² + 2as

These three equations of motion let us calculate any one quantity if we know the others. They are used constantly in physics and engineering problems.

A force is simply a push or a pull. A force can set a still object moving, stop a moving object, change its speed or direction, or change its shape.

Closely linked is inertia, the natural tendency of an object to resist any change in its state of rest or motion. A heavier object has more inertia: it is harder to start moving and harder to stop. Mass is the measure of inertia: the greater the mass, the greater the inertia.

One force acts on almost every moving object on Earth. Friction is the force that opposes relative motion between two surfaces in contact. It is the reason a rolling ball slows down and stops on its own. Friction takes three forms:

• Static friction: acts between surfaces that are in contact but not yet sliding. It must be overcome to start motion.
• Sliding friction: acts when one surface slides over another. It is somewhat smaller than static friction.
• Rolling friction: acts when one body rolls over another. It is much smaller than sliding friction.

Because rolling friction is the weakest of the three, machines are designed to roll rather than slide. Ball bearings apply this idea. Small steel balls are placed between the wheel and the axle in bicycles, cars and other machines. The balls replace sliding friction with rolling friction and reduce the effective area of contact between the moving parts. The result is far less friction, less wear and an easier-turning wheel.

Newton's first law of motion states that an object at rest stays at rest, and an object in motion keeps moving in a straight line at a constant speed, unless acted upon by an unbalanced force.

This is also called the law of inertia, because it describes inertia in action. It explains everyday experiences. When a bus brakes suddenly, the passengers lurch forward. Their bodies tend to keep moving even as the bus stops.

Newton's second law connects force to the change it produces. It states that the rate of change of momentum of an object is proportional to the applied force and happens in the direction of the force.

Momentum is the product of mass and velocity (p = mv). From this law comes the famous equation:

Force = mass × acceleration (F = ma)

So the same force gives a small mass a large acceleration but a large mass only a small one. This is why it is harder to push a loaded cart than an empty one.

Newton's third law states that for every action there is an equal and opposite reaction. Forces always occur in pairs: if object A pushes on object B, then B pushes back on A with an equal force in the opposite direction.

Examples are everywhere. A swimmer pushes the water back and is propelled forward. A gun recoils when fired. A rocket is thrust upward as it pushes gases downward. The two forces act on different objects, so they do not simply cancel out.

A powerful consequence of Newton's laws is the law of conservation of momentum: when no external force acts on a system, its total momentum stays constant.

In a collision, the total momentum before equals the total momentum after. When a moving ball strikes a stationary one, the momentum lost by the first is gained by the second. The recoil of a gun works the same way. The forward momentum of the bullet equals the backward momentum of the gun.

In science, work is done only when a force moves an object in the direction of the force. If there is no movement, or the force is at right angles to the motion, no work is done. Simply holding a heavy bag still does no scientific work.

Work is calculated as:

Work = Force × distance moved in the direction of the force

It is measured in joules (J). Work can be positive (force and motion in the same direction) or negative (force opposing motion, like friction).

Energy is the capacity to do work, also measured in joules. Its two main mechanical forms are:

• Kinetic energy: the energy of a moving object. A faster or heavier object has more kinetic energy.
• Potential energy: stored energy due to position or state. A stone held high, a stretched bow or a compressed spring all have potential energy.

Energy exists in many other forms too, including heat, light, sound, chemical, electrical and nuclear. One form can change into another.

A fundamental law of nature is the law of conservation of energy: energy can be transformed from one form to another, but it can neither be created nor destroyed. The total energy always stays the same.

For example, a falling ball steadily converts its potential energy into kinetic energy. But the total energy (potential + kinetic) remains constant throughout the fall (ignoring air resistance). This law governs all energy changes in the universe. It is the energy counterpart of the conservation of momentum described above.

Two machines may do the same work, but one may do it faster. Power measures the rate of doing work: how much work is done, or energy used, per unit time:

Power = Work ÷ Time

Power is measured in watts (W): one watt is one joule per second. A more powerful engine or appliance does work more quickly. Larger units include the kilowatt (1000 W). Electrical energy is often billed in kilowatt-hours.