Motion & Laws of Motion

Whether a body is at rest or in motion is never absolute — it always depends on the observer and the reference point chosen.

• A body is in motion if its position changes with time relative to its surroundings.
• Rest and motion are relative terms — there is nothing like absolute rest or absolute motion.
• A passenger sitting in a moving train is at rest with respect to the train but in motion with respect to the ground.
• The point or object chosen to describe motion is called the reference point or origin.
• The Earth itself is in motion, so a body "at rest" on Earth is still moving through space.

When a body moves it covers a path, and we can describe that journey either by the total length travelled or by the straight-line gap between start and finish.

• Displacement is the shortest straight-line distance between the initial and final positions, with direction.
• Distance is a scalar quantity; displacement is a vector quantity.
• Distance can never be negative or zero for a moving body, but displacement can be zero.
• Displacement is zero if the body returns to its starting point.
• Distance is always greater than or equal to displacement (distance ≥ displacement).
• The SI unit of both is the metre (m).

Physical quantities split into two families depending on whether direction matters in describing them.

• A vector has both magnitude and direction.
• Scalars are added by simple arithmetic, while vectors are added by special rules (the triangle or parallelogram law).
• Examples of scalars: distance, speed, mass, time, temperature, work, energy, power, density and electric charge.
• Examples of vectors: displacement, velocity, acceleration, force, momentum, weight and electric field.

How fast a body moves can be stated either as a plain rate or as a rate with a direction attached.

• Speed = distance ÷ time and its SI unit is metre per second (m/s).
• Velocity is the displacement per unit time; it is a vector.
• Velocity = displacement ÷ time and its SI unit is also m/s.
• Speed can never be negative; velocity can be positive, negative or zero.
• Average speed = total distance ÷ total time, while average velocity = total displacement ÷ total time.
• Uniform speed means equal distances in equal intervals of time.
• Uniform velocity means equal displacements in equal intervals in the same direction.
• To convert, 1 m/s = 3.6 km/h and 1 km/h = 5/18 m/s.

When the velocity of a body changes, we measure how quickly it changes through acceleration.

• Acceleration (a) = (final velocity − initial velocity) ÷ time = (v − u) ÷ t.
• The SI unit of acceleration is m/s².
• Acceleration is positive when velocity increases with time.
• Retardation (deceleration) is negative acceleration, occurring when velocity decreases with time.
• Uniform acceleration means velocity changes by equal amounts in equal intervals of time.
• A body falling freely under gravity has acceleration g = 9.8 m/s² (about 9.8 m/s² near the Earth's surface).
• In uniform circular motion, speed is constant but velocity changes (direction changes), so the body is still accelerating.

Bodies move in several distinct patterns, and recognising the type of motion helps describe it correctly.

• Rotatory motion — the body spins about a fixed axis, e.g. a spinning top or a fan.
• Oscillatory (vibratory) motion — the body moves to and fro about a fixed point, e.g. a pendulum or a swing.
• Circular motion — the body moves along a circular path, e.g. the Moon around the Earth.
• Periodic motion — motion that repeats itself after equal intervals of time, e.g. the hands of a clock.
• Random motion — motion with no fixed path or direction, e.g. the motion of gas molecules.

For a body moving with uniform acceleration in a straight line, three equations connect its initial velocity, final velocity, acceleration, time and displacement.

• s = ut + ½at² — second equation (position–time relation).
• v² = u² + 2as — third equation (velocity–position relation).
• Here u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement.

• v = u + gt, h = ut + ½gt² and v² = u² + 2gh — replacing a with g and s with height h.
• For a body dropped from rest, u = 0, so v = gt, h = ½gt² and v² = 2gh.
• The value of acceleration due to gravity g = 9.8 m/s² (taken as 9.8 m/s² or 9.81 m/s² in exams).

Sir Isaac Newton stated three fundamental laws that govern how forces affect the motion of bodies.

• A body at rest stays at rest, and a body in motion stays in uniform motion in a straight line, unless an external force acts on it.
• It defines force as that which changes a body's state of rest or motion.
• Example: dust falls off a carpet when it is beaten, because the carpet moves but the dust stays at rest due to inertia.

• The second law gives the measure of force: F = ma — Force = mass × acceleration.
• Force is directly proportional to the rate of change of momentum, F = Δp/Δt.
• The SI unit of force is the newton (N), where 1 N = 1 kg·m/s².
• One newton is the force that gives a 1 kg mass an acceleration of 1 m/s².
• Example: it is harder to stop a heavy truck than a light bicycle moving at the same speed.

• Every action has an equal and opposite reaction.
• Action and reaction act on two different bodies, so they never cancel each other.
• A swimmer pushes the water backward and the water pushes the swimmer forward.
• A rocket moves up by pushing hot gases downward (jet and rocket propulsion).
• Walking is possible because we push the ground backward and the ground pushes us forward.

Inertia is the natural tendency of a body to resist any change in its state of rest or of motion.

• Inertia depends only on the mass of a body — the greater the mass, the greater the inertia.
• Mass is the measure of inertia of a body.

The "quantity of motion" carried by a moving body is measured by its momentum, which combines how heavy it is with how fast it moves.

• Momentum is a vector quantity and its direction is that of the velocity.
• The SI unit of momentum is kg·m/s.
• A heavy body moving fast has large momentum; a light, slow body has small momentum.

• The law of conservation of momentum states that the total momentum of an isolated system stays constant in the absence of an external force.
• Total momentum before collision = total momentum after collision.
• m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ for two colliding bodies.
• The recoil of a gun is explained by conservation of momentum.
• Rocket and jet propulsion obey the conservation of momentum.

A force is a push or a pull that can change the state, shape or direction of motion of a body.

• Force is a vector quantity with SI unit newton (N).
• A force can change the speed, direction or shape of a body.

• Gravitational force is the weakest of the fundamental forces but acts over very long ranges.
• Friction and muscular force are contact forces.
• Magnetic, electrostatic and gravitational forces are non-contact (field) forces.
• Weight is the gravitational force on a body: W = mg.

Friction is the force that opposes the relative motion between two surfaces in contact, and it is a familiar everyday force.

• Friction always acts opposite to the direction of motion (or attempted motion).
• Friction arises due to the roughness and interlocking of surfaces in contact.
• Friction produces heat, which is why rubbing hands warms them.

• Static friction > sliding friction > rolling friction.
• Rolling friction is the least, which is why wheels and ball bearings are used.

• Friction lets us walk without slipping.
• Brakes of vehicles work because of friction.
• Writing with a pen or pencil is possible due to friction.
• Friction helps in fixing nails and tying knots.

• Friction wears out machine parts and tyres.
• Friction wastes energy as heat and lowers efficiency.
• Friction produces unwanted noise and heat in machines.

• Using lubricants (oil and grease) between moving parts.
• Using ball bearings or roller bearings to convert sliding into rolling friction.
• Polishing and smoothing the surfaces in contact.
• Streamlining the shape of vehicles, ships and aircraft to reduce air and water friction.
• Using air cushions (as in hovercraft) to avoid surface contact.

When a body moves along a circular path, two oppositely directed forces are commonly discussed — one real and one apparent.

• Centripetal force = mv²/r — where m = mass, v = speed, r = radius of the path.
• Centripetal force is a real force (provided by gravity, tension, friction, etc.).
• Centrifugal force acts away from the centre (outward) and is an apparent (pseudo) force.
• Centrifugal force appears only in a rotating frame of reference and is not a real force.

• The gravitational pull of the Sun provides the centripetal force for the planets.
• A cream separator and a washing-machine dryer use the centrifugal effect.
• Roads are banked at curves to provide the centripetal force safely.
• A stone tied to a string and whirled around flies off tangentially when the string breaks (inertia of direction).