An object remains at rest or continues moving at constant velocity unless acted upon by a resultant (net) force.
Newton's Second Law
The resultant force on an object is directly proportional to its acceleration and acts in the same direction. F = ma.
Newton's Third Law
When object A exerts a force on object B, object B exerts an equal and opposite force on object A. Forces always occur in pairs acting on different objects.
F = maF = resultant force (N) · m = mass (kg) · a = acceleration (m/s²)
Worked example
A 1200 kg car accelerates at 2.5 m/s². Find the resultant force.
F = ma = 1200 × 2.5 = 3000 N
Newton's Third Law pairs
The force pair must: act on different objects, be the same type of force, be equal in magnitude, and be opposite in direction. "The ground pushes up on the person with the same force that the person pushes down on the ground."
2. Resultant Forces
The resultant force is the single force that has the same effect as all the individual forces acting together. Add forces in the same direction; subtract forces in opposite directions.
Worked example
A 60 N driving force acts forward. A 25 N friction force acts backward. Find the resultant force.
Resultant = 60 − 25 = 35 N forward
For forces at right angles, use Pythagoras: resultant = √(F₁² + F₂²).
3. Friction
Friction is a force that opposes relative motion between surfaces in contact. It acts opposite to the direction of motion or intended motion.
Situation
Effect of friction
Sliding friction (kinetic)
Opposes motion; converts kinetic energy to heat
Static friction
Prevents an object from starting to move
Air resistance (fluid friction)
Increases with speed; opposes motion through air
When friction is useful
Braking, walking, holding objects, tyres gripping road — all rely on friction. Lubricants reduce friction by keeping surfaces separated.
4. Equilibrium
An object is in equilibrium when the resultant force on it is zero. This means it is either stationary or moving at constant velocity (Newton's First Law).
All upward forces = all downward forces
All leftward forces = all rightward forces
For rotation: sum of clockwise moments = sum of anticlockwise moments
Common mistake
Students write "the object is in equilibrium so there are no forces acting on it." Wrong — there are forces, but the resultant is zero. A book on a table has weight downward and normal reaction upward — two forces, resultant zero.
Newton's 2nd Law
F = ma
F in newtons (N), m in kilograms (kg), a in m/s2. F is the RESULTANT (net) force.
Must-Know for Exam
Newton's 1st Law: no resultant force = no change in motion (rest OR constant velocity)
Newton's 2nd Law: F = ma. F is RESULTANT force, not just any force.
Newton's 3rd Law: action-reaction pairs act on DIFFERENT objects, same magnitude, opposite direction
Weight W = mg (g = 10 N/kg). Mass is constant; weight depends on gravitational field strength.
Free body diagram: draw ALL forces on ONE object with arrows showing direction and size
5. Common Exam Traps
Trap 1 — Newton's Third Law pairs
Both forces must act on DIFFERENT objects. "The table pushes up on the book, and the book pushes down on the table" is a correct Newton's Third Law pair. "Weight and normal reaction on the same book" is NOT a Newton's Third Law pair.
Trap 2 — Constant velocity ≠ no force
A car moving at constant 60 km/h on a motorway still has engine force and friction. They are balanced (resultant = 0), not absent.
Trap 3 — F = ma uses resultant force
The F in F = ma is the RESULTANT (net) force — not just one of the forces acting. Always subtract opposing forces before applying the equation.
Key Terms — Flashcard Review
Tap each card to reveal the definition.
Newton's 1st Law
An object remains at rest or moves with constant velocity unless acted on by a resultant force.
Newton's 2nd Law
F = ma. Resultant force = mass x acceleration. The larger the force, the greater the acceleration.
Newton's 3rd Law
For every action force, there is an equal and opposite reaction force on a DIFFERENT object.
Weight
Gravitational force on an object. W = mg. Unit: newton (N). Acts downward from centre of gravity.
Friction
Resistive force opposing relative motion between surfaces. Always acts opposite to direction of motion.
Terminal velocity
When driving force equals resistive force (air resistance/drag). Resultant force = 0, so constant velocity.
🎯 Practice Quiz — Test Yourself
8 O Level-style questions on this topic. Select an answer to see instant feedback.
Question 1 of 8
An unbalanced force acting on an object causes it to:
Explanation: Newton's 2nd Law: a net (unbalanced) force causes acceleration — a change in velocity (speed or direction).
Question 2 of 8
A 5 kg object accelerates at 3 m/s². What is the net force?
Explanation: F = ma = 5 × 3 = 15 N.
Question 3 of 8
Newton's 3rd law pair forces act on:
Explanation: Newton's 3rd law pairs ALWAYS act on different objects: same magnitude, opposite direction, same type of force.
Question 4 of 8
A 60 kg person stands in a lift accelerating upward at 2 m/s². The normal force is: (g = 10 m/s²)
Explanation: N − W = ma → N = m(g+a) = 60(10+2) = 720 N. Accelerating upward means N > W.
Question 5 of 8
Friction always acts:
Explanation: Friction opposes relative motion (or tendency to move). Always acts opposite to motion.
Question 6 of 8
A 5 kg object accelerates at 3 m/s2. The resultant force on it is:
Explanation: F = ma = 5 x 3 = 15 N. Always use resultant (net) force in F = ma, not just one of the forces acting.
Question 7 of 8
A skydiver reaches terminal velocity when:
Explanation: Terminal velocity: as the skydiver speeds up, air resistance increases until it equals weight. Resultant force = 0. By Newton's 1st law, velocity is then constant (terminal velocity). Acceleration becomes zero.
Question 8 of 8
A book rests on a table. Which pair correctly describes Newton's 3rd Law reaction to the table's normal force on the book?
Explanation: Newton's 3rd Law: the table pushes UP on the book (normal force). The reaction pair is the book pushing DOWN on the table with the same magnitude. These act on DIFFERENT objects (table acts on book; book acts on table).
Original study notes for Singapore students. Not affiliated with MOE, SEAB or Cambridge. Use alongside your school notes and official syllabus documents.