Motion and Force

An object is said to be in motion when it changes its position with respect to its surroundings over time. To describe motion clearly, scientists use a set of carefully defined quantities. These quantities fall into two groups. A scalar quantity has only magnitude (size) — for example, distance, speed, mass, and time. A vector quantity has both magnitude and direction — for example, displacement, velocity, and force. Understanding this distinction is the key to describing motion correctly.

Distance is the total length of the path actually travelled by an object, regardless of direction. It is a scalar, so it is never negative. Displacement is the shortest straight-line distance from the starting point to the final point, measured in a particular direction. It is a vector. If a person walks 4 m east and then 3 m back west, the distance covered is 7 m, but the displacement is only 1 m east. If an object returns to its starting point, its displacement is zero even though the distance covered is not.

Speed tells us how fast an object moves — it is the distance travelled per unit time, and it is a scalar. Speed is calculated as distance divided by time, and its SI unit is the metre per second (m/s). Velocity is the displacement per unit time in a stated direction — it is a vector that tells us both how fast and in which direction an object moves. Its unit is also metre per second, but velocity must include a direction (for example, "5 m/s towards the north").

The difference matters in real situations. A car going around a circular track at a steady 40 km/h has a constant speed, but its velocity keeps changing because its direction keeps changing. So an object can move with constant speed and still have a changing velocity. These ideas of distance, displacement, speed, and velocity form the foundation for studying all kinds of motion.

The motion of an object can be steady or changing, and we classify it accordingly. Uniform motion is motion in which an object covers equal distances in equal intervals of time, however small the intervals. For example, a car travelling exactly 20 m every second is in uniform motion — its speed stays constant. Non-uniform motion is motion in which an object covers unequal distances in equal intervals of time, so its speed keeps changing. A car in city traffic that speeds up, slows down, and stops is in non-uniform motion.

When the speed of an object changes, we say it is accelerating. Acceleration is the rate at which the velocity of an object changes with time. If the speed increases, the acceleration is positive; if the speed decreases (the object slows down), the change is called deceleration or retardation. An object in uniform motion has zero acceleration because its speed does not change.

Motion can be shown clearly using graphs. A distance-time graph plots the distance travelled (on the vertical axis) against time (on the horizontal axis). For uniform motion, the distance-time graph is a straight, slanting line, because equal distances are covered in equal times. The steeper the line, the greater the speed. For an object at rest, the line is horizontal (distance does not change). For non-uniform motion, the distance-time graph is a curved line, because the distance covered each second keeps changing.

A speed-time graph plots speed against time. For uniform speed, this graph is a horizontal straight line, since the speed stays the same. For uniformly increasing speed (constant acceleration), it is a slanting straight line going upward. Graphs are powerful because, at a glance, they reveal whether an object is at rest, moving uniformly, speeding up, or slowing down, and they let us compare the motion of different objects.

A force is a push or a pull acting on an object. Force is a vector quantity, having both magnitude and direction, and its SI unit is the newton (N). A force can do several things to an object: it can make a stationary object move, stop a moving object, change the speed or direction of a moving object, and change the shape or size of an object. The motion of objects under the action of forces was explained by Sir Isaac Newton in his three famous laws of motion.

Newton's First Law of Motion states that an object at rest stays at rest, and an object in motion continues to move at a constant speed in a straight line, unless acted on by an external force. This natural tendency of an object to resist a change in its state of rest or motion is called inertia. A heavier object has more inertia. The first law explains why passengers lurch forward when a moving bus brakes suddenly (their bodies tend to keep moving) and why we feel pushed back when a vehicle starts suddenly. This is why seat belts are important.

Newton's Second Law of Motion relates force, mass, and acceleration. It states that the acceleration produced in an object is directly proportional to the force applied and takes place in the direction of the force. This is summed up in the famous equation Force = mass × acceleration (F = ma). The law tells us that a larger force produces a greater acceleration, and that for the same force, a heavier object accelerates less. This is why it is harder to push a loaded cart than an empty one.

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. Forces always act in pairs: when one object exerts a force on a second object, the second exerts an equal force back in the opposite direction. This explains why a swimmer pushes water backward to move forward, why a gun recoils when fired, and how a rocket is propelled upward by pushing hot gases downward. Together, these three laws describe how all everyday objects move under forces.

Whenever one surface moves or tends to move over another surface, a force acts to oppose this motion. This opposing force is called friction. Friction always acts in the direction opposite to the motion (or attempted motion) of an object. Friction is caused by the irregularities and roughness of the two surfaces in contact: even surfaces that look smooth have tiny bumps and hollows that interlock and resist sliding. The rougher the surfaces and the harder they are pressed together, the greater the friction.

There are three main types of friction. Static friction is the friction that acts when an object is at rest and a force is trying to move it; it must be overcome before the object starts to move. Kinetic (sliding) friction acts when an object is actually sliding over a surface. Rolling friction acts when an object rolls over a surface, such as a wheel or a ball. An important fact is that rolling friction is much smaller than sliding friction, which is why wheels and ball-bearings are used to move heavy loads easily.

Friction is both a friend and a foe. Its advantages are many: friction lets us walk without slipping, allows vehicles to grip the road and brake, lets us write with a pen or pencil, helps us hold objects, and enables a matchstick to light when struck. Without friction, walking, gripping, and stopping would all be impossible. Its disadvantages are that it wears out the soles of shoes, tyres, and machine parts; it produces heat that can damage machinery; and it wastes energy, reducing the efficiency of machines.

Because friction has both good and bad sides, we sometimes need to increase it and sometimes to reduce it. Friction is increased by making surfaces rougher — for example, the treads (grooves) on tyres and the soles of shoes, and sand sprinkled on slippery ground. Friction is reduced by polishing surfaces, using lubricants such as oil and grease, using ball-bearings to convert sliding into rolling, and giving vehicles and aircraft a smooth streamlined shape to reduce friction with air and water.

When a force acts on a surface, its effect depends not only on the size of the force but also on the area over which it acts. Pressure is defined as the force acting per unit area of a surface. In symbols, Pressure = Force ÷ Area (P = F/A). The SI unit of pressure is the pascal (Pa), where one pascal is one newton per square metre. The formula shows that for the same force, a smaller area gives a larger pressure, and a larger area gives a smaller pressure. This is why a sharp knife (small area edge) cuts easily, why nails are pointed, and why a camel's broad feet stop it sinking into soft sand.

Gases and liquids also exert pressure. The thick layer of air surrounding the Earth presses on everything beneath it; this is called atmospheric pressure. Although we do not usually notice it, atmospheric pressure is large, and it acts in all directions. It is responsible for effects such as a drinking straw working (we reduce the pressure inside, and atmospheric pressure pushes the liquid up) and a rubber sucker sticking to a wall. Liquids exert pressure too, and this pressure increases with depth — which is why a dam is built much thicker at its base, where the water pressure is greatest. The principle that pressure applied to an enclosed liquid is transmitted equally in all directions is used in hydraulic systems such as car brakes and hydraulic lifts.

When an object is placed in a liquid, it experiences an upward force from the liquid. This upward force is called the buoyant force or upthrust, and the tendency of a liquid to push an object upward is called buoyancy. This is why objects feel lighter in water and why we can lift a heavy stone more easily under water than in air.

The relationship was stated by the ancient Greek scientist Archimedes. Archimedes' Principle states that when an object is fully or partly immersed in a liquid, it experiences an upthrust equal to the weight of the liquid displaced by the object. From this we get the conditions for floating and sinking: an object floats if it is less dense than the liquid (the upthrust can support its weight), and it sinks if it is denser than the liquid. This is why a cork floats but a coin sinks in water, and why huge steel ships float — their hollow shape makes their average density less than that of water.