OCR GCSE Physics A: Interacting forces, vectors and free body diagrams (J249)

This guide covers statements P2.2a to P2.2h and P2.2p of the OCR GCSE (9-1) Gateway Science Physics A specification (J249, Version 5.0, July 2026, for first assessment in 2018). They sit in topic P2, section P2.2 Newton’s laws. None of these statements is marked Higher Tier only, so all of this content is for both tiers. Newton’s second law, inertia, momentum and circular motion are taught separately, as are work done, stored energy and power.

Use the revision notes for quick recall and the practice questions to test yourself. The wider topic is in OCR GCSE Physics: Forces, with its practice set. See the OCR GCSE Physics hub and the printable checklist. Not sure where you stand? Try the free 10-minute diagnostics.

What this unit covers

Statement	What you must be able to do
P2.2a	Recall ways objects interact: electrostatics, gravity, magnetism and contact (including normal contact force and friction)
P2.2b	Describe how each interaction involves a pair of objects, producing a force on each
P2.2c	Represent forces as vectors, drawing free body diagrams
P2.2d	Apply Newton’s first law to uniform velocity and to changes of speed and/or direction (qualitative only)
P2.2e	Use vector diagrams for resolution, resultant force and equilibrium (scale drawings limited to parallel and perpendicular vectors)
P2.2f	Describe forces on an isolated solid object or system, for example terminal velocity
P2.2g	Use free body diagrams where two or more forces give a resultant
P2.2h	Use free body diagrams where forces balance to give zero resultant (qualitative only)
P2.2p	Recall and apply Newton’s third law to equilibrium and non-equilibrium situations

Forces come from interactions (P2.2a, P2.2b)

A force is a push or pull that one object exerts on another. It is measured in newtons (N). Forces never exist alone: each one belongs to an interaction between two objects.

Contact interactions need the objects to touch:

• normal contact force: the push of a surface on an object resting on or pressing against it, always at right angles to the surface
• friction: the force between surfaces that opposes sliding, or the tendency to slide

Non-contact interactions act across a gap:

• gravity: pulls masses together, so Earth pulls you down
• electrostatics: charged objects attract or repel
• magnetism: magnets attract or repel, and attract magnetic materials

Each interaction involves two objects, and each object feels a force. When a magnet pulls a nail, the nail also pulls the magnet. When Earth pulls a stone, the stone pulls Earth. To describe an interaction fully, name both objects and both forces.

A useful wording pattern is “force of A on B” and “force of B on A”. For example: “the force of the brush on the wall” and “the force of the wall on the brush”.

Forces as vectors (P2.2c)

A vector has both size and direction. A force is a vector. In a diagram:

• the length of the arrow shows the size, using a stated scale
• the direction of the arrow shows the direction of the force
• the arrow starts at the object, or at the point where the force acts

Forces in opposite directions along a line are given opposite signs when you add them. Always state which direction you are treating as positive.

Free body diagrams (P2.2c, P2.2f, P2.2g, P2.2h)

A free body diagram shows one object only, drawn as a box or dot, with arrows for only the forces acting on that object. Rules that gain credit:

1. Isolate the object. Do not draw the surface or other objects.
2. Draw every force as an arrow from the object, labelled with its name (weight, normal contact force, friction, drag, thrust, tension).
3. Make arrow lengths match the sizes. Equal forces get equal lengths.
4. Do not draw forces that the object exerts on something else.
5. Do not draw the resultant as an extra arrow among the forces. State it separately.

A book on a table:

        normal contact force (from table)
                  ^
                  |
              [ book ]
                  |
                  v
        weight (from Earth)

The two arrows are the same length because the book is not accelerating vertically.

Forces on an isolated object or system. A system is a chosen object or group treated as one thing. A car being driven forward at constant speed on a flat road has:

• thrust (driving force) forward
• drag and friction backward
• weight down
• normal contact force up

Newton’s first law (P2.2d)

A resultant force of zero means an object that is at rest stays at rest, and an object that is moving keeps its speed and direction. Only a non-zero resultant force changes the motion.

Qualitative ideas you must be able to apply:

• Resultant force zero: the object is stationary or moves with uniform velocity. Constant velocity needs no resultant force. A car at steady speed has driving force equal to resistive forces.
• Resultant force not zero: the velocity changes. That means speed changes, direction changes, or both.
• A moving object does not need a force to keep going. It needs a resultant force to change what it is doing.

A common misconception is that a stationary object has no forces on it. It has forces, and they balance.

The specification suggests measuring the velocity of ball bearings in glycerol (at different temperatures or of differing sizes), and designing a parachute and measuring its terminal velocity as it is dropped.

Terminal velocity (P2.2f)

A falling skydiver starts with weight larger than drag, so the resultant is downward and speed rises. As speed rises, drag rises. The resultant shrinks. When drag equals weight, the resultant is zero and the skydiver falls at constant velocity: terminal velocity. Opening the parachute raises drag above weight. The resultant is then upward, so the skydiver slows until drag again equals weight, at a smaller terminal velocity. The same ideas apply to a vehicle: top speed is reached when drag and friction equal the driving force.

Resultant forces (P2.2e, P2.2g)

The resultant force is one force that could replace all the forces on the object and give the same overall effect.

Forces along one line. Add forces in the same direction. Subtract those in opposite directions.

Worked example 1. A crate is pushed east with 260 N. Friction of 180 N acts west. The weight and normal contact force are equal and opposite.

• Horizontal resultant = 260 − 180 = 80 N east.
• Vertical resultant = 0 N.

Forces at right angles. Draw a scale drawing, placing the arrows head to tail. The resultant is the arrow that completes the right-angled triangle. Pythagoras gives the size, and a protractor or tan gives the angle.

Worked example 2. A boat is pulled by a 15 N force east and an 8.0 N force north.

Scale: 1 cm represents 2 N, so the arrows are 7.5 cm and 4.0 cm.

• Draw 7.5 cm east. From its end, draw 4.0 cm north.
• Join the start to the end. The line measures 8.5 cm, which is 17 N.
• Check: √(15² + 8.0²) = √289 = 17 N.
• Angle north of east: tan⁻¹(8.0 / 15) = 28° (to 2 significant figures).

Resolution of forces (P2.2e)

Resolving does the reverse: a single force is replaced by two perpendicular forces (components) that together have the same effect. Scale drawings are limited to parallel and perpendicular vectors, so you draw the force as the diagonal of a rectangle and read off the sides.

Worked example 3. A rope pulls a trolley with 100 N, at an angle such that the force makes a 3-4-5 triangle with the ground. The horizontal side is 4 units and the vertical side is 3 units.

Scale: 1 cm represents 10 N.

• Draw the 100 N arrow as 10 cm long, at the correct angle.
• Draw a horizontal line and a vertical line to make a right-angled triangle.
• The horizontal side measures 8.0 cm, so the horizontal component is 80 N.
• The vertical side measures 6.0 cm, so the vertical component is 60 N.
• Check: 80² + 60² = 10 000, and √10 000 = 100 N.

The horizontal component pulls the trolley along. The vertical component partly lifts the trolley, so the ground pushes up with a smaller normal contact force than the weight.

Equilibrium and balanced forces (P2.2e, P2.2h)

An object is in equilibrium when the resultant force is zero. The forces balance: for every force in one direction there are forces totalling the same size in the opposite direction. A vector diagram of forces in equilibrium forms a closed shape: the arrows, placed head to tail, return to the start.

Worked example 4. A ring is pulled with 6.0 N east and 8.0 N north. What third force keeps it in equilibrium?

• The resultant of the two forces: √(6.0² + 8.0²) = 10 N.
• The angle north of east is tan⁻¹(8.0 / 6.0) = 53°.
• The third force must be equal and opposite to this resultant: 10 N, pointing 53° south of west.
• The three arrows drawn head to tail form a closed triangle.

A skydiver at terminal velocity, a hovering helicopter and a cyclist at a steady speed on a flat road are all in equilibrium. Equilibrium does not mean “not moving”. It means “not accelerating”.

Worked example 5 (non-equilibrium, then equilibrium). A car has 3150 N of driving force forward and 2550 N of resistive forces backward. The resultant is 3150 − 2550 = 600 N forward, so the speed rises. At a higher speed, the resistive forces reach 3150 N. The resultant is then 0 N and the car continues at constant velocity.

Newton’s third law (P2.2p)

If object A exerts a force on object B, then B exerts a force on A of the same size and type, in the opposite direction.

An interaction pair (third-law pair) has these properties:

• the two forces act on different objects
• they are the same size
• they are in opposite directions
• they are the same kind of force, for example both gravitational

Example: the Earth pulls a book down with a gravitational force. The book pulls the Earth up with a gravitational force of equal size.

A book’s weight and the table’s push on it are not a third-law pair. They act on the same object and they are different kinds of force. The pair for the normal contact force of the table on the book is the contact force of the book on the table.

Application to equilibrium. A book at rest on a table has balanced forces because the weight and the normal contact force have equal size on the book. That is the first law, not the third.

Application to non-equilibrium. A girl on a skateboard pushes a wall with 45 N. The wall pushes her with 45 N, in the opposite direction. Each force acts on a different object, so they cannot cancel. The 45 N on the girl is unbalanced if nothing else acts horizontally, so she moves away from the wall.

For a rocket, the engine pushes exhaust gas backward and the gas pushes the rocket forward with an equal force.

Common errors

• Calling weight and normal contact force a third-law pair.
• Adding third-law forces to get zero. They act on different objects.
• Drawing forces the object exerts on other things in a free body diagram.
• Saying “constant velocity needs a constant force”. It needs zero resultant force.
• Reading the resultant of perpendicular forces by adding the sizes (15 + 8 = 23 N) instead of using Pythagoras.
• Leaving out units, or leaving out the direction of the resultant.
• Saying terminal velocity means “no forces”. The forces balance.

Official syllabus

OCR GCSE (9-1) Gateway Science Physics A (J249), Version 5.0, July 2026, for first assessment in 2018, published by OCR: statements P2.2a to P2.2h and P2.2p.