Newton's laws — OCR GCSE Physics

Momentum is a vector quantity that measures how hard it is to stop a moving object. For Higher tier you recall and apply p = m × v, where momentum p is in kilogram metres per second (kg m/s), mass m is in kilograms (kg) and velocity v is in metres per second (m/s). Because velocity carries direction, momentum does too: a 2 kg ball moving at 3 m/s to the right has momentum 6 kg m/s to the right, while the same ball moving at 3 m/s to the left has momentum 6 kg m/s to the left. Convert grams to kilograms and cm/s or km/h to m/s before substituting, then multiply mass by velocity and attach the correct unit and direction.

Work done measures the energy transferred when a force moves an object. You recall and apply W = F × d, where work done W is in joules (J), force F is in newtons (N) and distance d is in metres (m). The distance must be measured along the line of action of the force, so only the part of the movement in the direction of the force counts. Lifting a 20 N box 1.5 m upwards does 20 × 1.5 = 30 J of work, because the lift is along the line of the weight. Pushing a box sideways while it moves forward does no work in the forward direction if the push is at right angles to the motion. Convert centimetres to metres and kilonewtons to newtons before multiplying.

Power measures how quickly work is done, so a machine that transfers 600 J in 3 s has a power of 600 J ÷ 3 s = 200 W. The equation power (W) = work done (J) / time (s) links three quantities: work done in joules, time in seconds and power in watts, where 1 W = 1 J/s. To apply it, identify the work done and the time taken, divide, and give the answer in watts. To rearrange, multiply power by time to find work done, or divide work done by power to find time. Always convert milliseconds or minutes to seconds before dividing, and check that a larger power for the same work means a shorter time.

Objects interact when a force acts between them, and the specification names five routes: electrostatics, gravity, magnetism, and contact through the normal contact force and through friction. A charged balloon attracting small paper pieces is an electrostatic interaction acting at a distance. The Earth pulling a falling apple is a gravitational interaction. Two magnets repelling or attracting illustrate magnetism. A book resting on a table experiences a normal contact force pushing perpendicular to the surface, while a box sliding across a floor is slowed by friction acting along the surface. Non-contact interactions (electrostatics, gravity, magnetism) act without touching; contact interactions require surfaces to press or rub together.

Forces never come alone: they arise from an interaction between two objects, and each object in the pair experiences a force. If you push a wall, your hand pushes the wall and the wall pushes back on your hand with an equal-sized force in the opposite direction. The same pattern appears when a swimmer pushes water backwards and the water pushes the swimmer forwards, and when the Earth pulls a falling ball downwards while the ball pulls the Earth upwards. To describe an example, name both objects, state the direction of the force each one exerts on the other, and note that the two forces are equal in size and opposite in direction. The two forces act on different objects, so they never cancel each other out.

A vector has both magnitude and direction, so a force is fully described only when you give its size in newtons and the direction in which it acts. A free body force diagram isolates one object and shows every force acting on that object as an arrow: the arrow's length represents the force's magnitude and the arrowhead gives its direction. Draw each arrow starting from the object or from a labelled point on it, and label each force (for example weight, normal contact force, friction, tension, thrust). Choose a scale so lengths are comparable, and draw opposing forces along the same line. If arrows are equal and opposite the forces balance and the resultant is zero; if not, the resultant is found by vector addition. A moving object at constant velocity still has balanced forces, so no resultant arrow is needed.

Newton's first law says an object keeps a constant velocity unless a resultant force acts on it. To apply it, isolate one body, list the forces on that body only, then combine them to judge the resultant. If the forces balance, the resultant is zero and the object continues at uniform velocity, or stays at rest. If they do not balance, a resultant force exists and the speed and/or direction change: the object accelerates, slows, or curves. For example, a car cruising at a steady 20 m/s on a straight road has driving force balanced by friction and drag, so its velocity is constant. When the driver brakes, friction exceeds the driving force, a backward resultant acts, and the car slows. Reasoning stays qualitative: name the forces, state whether they balance, and link that to the motion.

Higher tier learners use vector diagrams to show three situations: resolving a force into components, finding a net (resultant) force, and showing equilibrium. Scale drawings are limited to parallel and perpendicular vectors, so you draw arrows to scale along two perpendicular directions. To resolve a force, draw it as the diagonal of a rectangle and read the two perpendicular components from the sides. To find a net force, add parallel vectors tip to tail and combine perpendicular ones with a right-angled triangle, measuring the resultant with a ruler and protractor. Equilibrium occurs when vectors close to form a complete shape, giving zero resultant. For example, a 5 N force at an angle resolves into a horizontal and a vertical component whose lengths you measure against the scale. Keep the scale consistent and state it on the diagram.

Treat the object or system as isolated and list only the forces acting on it, each with its direction. For a skydiver, weight acts downwards and drag acts upwards; drag grows with speed until it equals weight, so the resultant force becomes zero and the skydiver falls at constant terminal velocity. If the skydiver opens a parachute, drag increases, the resultant force acts upwards, the skydiver decelerates and settles at a lower terminal velocity. Apply the same reasoning to a vehicle: driving force forwards, resistive forces (air resistance and friction) backwards; at constant top speed these balance. Name each force, state its direction, and explain how the resultant changes the motion.

A free body diagram shows the object as a point or simple shape with one arrow for each force acting on it; arrow length represents magnitude and the arrowhead gives direction. When two or more forces act, combine them: forces along the same line add or subtract, so opposite forces partly cancel. If the total is not zero, a resultant force remains and the object accelerates in the direction of that resultant. For example, a box pushed with 30 N to the right while friction acts with 10 N to the left has a resultant of 20 N to the right. Read each diagram, resolve the arrows, and choose the option that correctly states the resultant's size and direction.

A free body diagram shows one chosen object as a point or simple shape with an arrow for every force acting on that object only. Each arrow points in the direction of the force, and arrow length represents magnitude. When the arrows cancel — equal and opposite along each line — the resultant force is zero. This is the balanced-force special case, and it is qualitative at Higher tier: you reason about balance and direction, not about calculating a value. Example: a book resting on a table has weight acting downwards and the normal contact force from the table acting upwards; equal magnitudes give a resultant of zero, so the book stays at rest. Example: a car travelling at constant velocity along a straight level road has driving force balanced by resistive forces and weight balanced by the normal reaction.

Newton's second law links resultant force F, mass m and acceleration a by the equation F = m × a. Force is measured in newtons (N), mass in kilograms (kg) and acceleration in metres per second squared (m/s²). A resultant force of 12 N on a 3 kg trolley gives a = F ÷ m = 12 N ÷ 3 kg = 4 m/s². Rearranging gives m = F ÷ a and a = F ÷ m, so any one quantity can be found from the other two. Always use the resultant force, not a single applied force, when several forces act: subtract opposing forces first. Convert grams to kilograms by dividing by 1000, for example 500 g = 0.5 kg. Check units before substituting, then state the unit with the answer. A larger resultant force on the same mass gives a larger acceleration, and a larger mass under the same force gives a smaller acceleration.

Inertia describes how strongly an object resists any change in its velocity, whether that change is a speeding up, a slowing down or a change of direction. A loaded trolley is harder to start, stop or turn than an empty one because it has more inertia. Inertial mass puts a number on this: it is defined as the ratio of force over acceleration, so m = F ÷ a. A larger inertial mass means a smaller acceleration for the same resultant force. The definition is a ratio, so the force must be the resultant force acting on the object and the acceleration must be measured in the same direction. Units follow from the ratio: newtons divided by metres per second squared give kilograms.

Momentum is a vector quantity defined as mass multiplied by velocity, p = m × v, measured in kilogram metres per second (kg m/s). Because velocity has direction, momentum has direction too: an object moving left has momentum in the opposite sense to one moving right. In a collision, the total momentum of the interacting objects before the collision equals the total momentum after it, provided no external resultant force acts on the system. This is the law of conservation of momentum. For example, two trolleys that collide and stick together share a combined momentum equal to the sum of their individual momenta before impact, allowing the combined velocity to be calculated. When objects move in opposite directions, treat one direction as positive and the other as negative before adding.

This separate-science criterion asks you to use formulae that link force, mass, velocity and acceleration, and to explain how a change in one quantity affects the others. Start from F = ma: a resultant force on a mass produces acceleration in the direction of that force, so doubling the force on a fixed mass doubles the acceleration, while doubling the mass under a fixed force halves it. Then connect acceleration to velocity change using a = (v − u) ÷ t, where u is initial velocity, v is final velocity and t is the time taken. Combining these gives F = m(v − u) ÷ t, which shows that a larger velocity change in a shorter time needs a larger force. Use consistent SI units: force in newtons (N), mass in kilograms (kg), velocity in metres per second (m/s) and acceleration in metres per second squared (m/s²).

This criterion asks you to calculate work done with W = F × s, where F is the force in newtons and s is the distance moved in metres along the line of action of that force, giving work done in joules (J). The distance must be measured in the same direction as the force: a force pushing a box 3 m across a floor does 60 J of work if the force is 20 N along the motion, but a force at right angles to the motion does no work because there is no movement along its line of action. Describe the energy transfer too: the work done by the pushing force transfers energy from the person to the box's kinetic energy store, and friction transfers energy by heating to the surroundings. One joule equals one newton metre, so 20 N × 3 m = 60 J.

This criterion asks you to do two linked things. First, calculate stored energy and energy transferred in a range of situations, choosing the right relationship for the context: gravitational potential energy from mass, gravitational field strength and height; kinetic energy from mass and speed; and work done by a force from force and distance moved along the force. Second, convert between newton-metres and joules. The key idea is that one newton-metre equals one joule, because a force of 1 N moving its point of application 1 m along its own line transfers 1 J. So a work-done answer of 240 N m is 240 J, and a stored energy of 0.75 J may be written as 0.75 N m. Keep units consistent, square the speed before halving and multiplying by mass, and check whether the question wants the value in joules or newton-metres.

Power measures how quickly energy is transferred, not how much energy is transferred in total. The definition is that power is the rate at which energy is transferred, so a device with a larger power transfers the same energy in less time, or more energy in the same time. Use examples to make this concrete. A 2000 W kettle transfers energy to water faster than a 1000 W kettle, so it boils the same amount of water in less time. A lift motor of higher power raises a load in a shorter time. Two lamps may transfer the same total energy, but the brighter, higher-power lamp does it in less time. When explaining, name the device, state the energy transfer involved, and compare the time taken or the energy per second, linking this back to the definition of power as a rate.

Newton's third law says that when body A exerts a force on body B, body B exerts an equal-sized force on A in the opposite direction. The two forces act on different objects, so they never cancel each other. A book resting on a table is in equilibrium because the upward push of the table on the book balances the downward pull of gravity on the book; both of those forces act on the book. The third-law partner of the book's weight is the book's gravitational pull on the Earth, not the table's push. In a non-equilibrium case, such as a rocket accelerating, the exhaust pushes the rocket forward while the rocket pushes the exhaust backward with an equal force.

Velocity is a vector: it has both a magnitude (the speed) and a direction. An object moving round a circle at constant speed keeps the same magnitude of velocity but its direction of motion changes continuously, because at each instant the motion is along the tangent to the circle. Since the direction changes, the velocity changes, even though the speed does not. A changing velocity means the object is accelerating, and that acceleration is directed towards the centre of the circle, produced by a resultant force acting towards the centre. This is a qualitative explanation only: no calculation of centripetal acceleration or force is required. For example, a car going round a roundabout at a steady speed has a changing velocity because its heading keeps turning, so a resultant force towards the centre acts on it.