Kinematics (Topic 2) describes how an object moves. Dynamics explains why it moves that way, by looking at the forces acting on it. These notes cover types of force, mass, weight and gravitational field strength, free-body diagrams, resultant force and equilibrium, Newton's three laws, and three forces in equilibrium solved with a closed force triangle.
Force, mass and weight are used again in Turning Effect of Forces, Pressure and Energy later in Sec 3–4, so the definitions must be learnt precisely. Examiners test whether you can apply Newton's laws: predict motion from forces, calculate with F = ma and identify action–reaction pairs.
What these notes cover
- •Force as a vector
- •Contact and non-contact forces
- •Mass and inertia
- •Gravitational field strength
- •Weight, and mass versus weight
- •Free-body diagrams: the 3-step method
- •Resultant force: collinear and perpendicular forces
- •Balanced and unbalanced forces: equilibrium
- •Three ways a resultant force changes motion
- •Newton's second law: F = ma
- •Action–reaction pairs (Newton's third law)
- •Three forces in equilibrium: closed force triangle
Key definitions
- Force
- A push or a pull that one body exerts on another. It is a vector quantity with both magnitude and direction, and its SI unit is the newton (N).
- Mass
- The amount of matter in a body; also the property of a body that resists a change in its state of rest or motion, called inertia. It is a scalar measured in kilograms (kg) and is constant everywhere.
- Weight
- The gravitational force acting on an object because of a gravitational field. It is a vector measured in newtons, acting vertically downward through the centre of gravity, and it changes with location.
- Resultant force
- The single force that has the same effect on a body as all the forces acting on it combined; the vector sum of all the forces on the body.
- Equilibrium
- A body is in equilibrium when the resultant force on it is zero. The forces are balanced and the body is either at rest or moving at constant velocity (constant speed in a straight line).
Key formulas
Gravitational field strength
g = W ÷ m
g is the gravitational force per unit mass in N/kg, W is the weight in N and m is the mass in kg. On Earth g ≈ 10 N/kg and on the Moon g ≈ 1.6 N/kg; always use the value the paper gives.
Weight
W = mg
Weight in N, mass in kg, g in N/kg. Mass stays the same everywhere, but weight changes because g changes with location.
Resultant of collinear forces
resultant force = (sum of forces in positive direction) − (sum of forces in negative direction)
Choose and state a positive direction first. A negative answer means the resultant points the opposite way; give the answer as a magnitude and direction, e.g. 15 N to the left.
Resultant of two perpendicular forces
F = √(F₁² + F₂²); tan θ = F₂ ÷ F₁
Use only when the two forces are at 90°. θ is measured from F₁, so state which direction the angle is measured from. For other angles, use a scale drawing.
Newton's second law
F = ma
F is the resultant force in N (not any single applied force), m is the mass in kg and a is the acceleration in m/s². The acceleration is always in the direction of the resultant force.
Scale conversion (force triangle)
force in N = length in cm × scale in N per cm
Always state the scale on the drawing, e.g. 1 cm : 5 N, and make the longest side roughly 6 cm to 10 cm.
Worked example
A skydiver of total mass 75 kg is falling vertically at a constant speed. Take g = 10 N/kg. (a) State the air resistance on the skydiver. Explain your answer. (b) The parachute opens, and the air resistance suddenly increases to 1200 N. Calculate the acceleration of the skydiver at this instant, and describe the effect on the motion.
- 1(a) Find the weight first: W = mg = 75 × 10 = 750 N downward.
- 2The speed is constant, so the resultant force is zero and the air resistance must balance the weight: the air resistance is 750 N upward.
- 3(b) Take upward as positive: resultant force = 1200 − 750 = 450 N upward.
- 4Apply F = ma: a = F ÷ m = 450 ÷ 75 = 6.0 m/s² upward.
- 5The skydiver is still moving downward, but the resultant force acts upward, opposite to the velocity, so the skydiver slows down.
Watch out: An upward acceleration here does not mean the skydiver starts moving upward; it means the downward speed decreases.
Common mistakes
Giving weight in kilograms
Wrong: My weight is 50 kg.
Right: 50 kg is a mass. The weight is 50 × 10 = 500 N.
Calling W and N an action–reaction pair
Wrong: The weight of a book on a table and the normal reaction from the table are an action–reaction pair.
Right: W and N act on the same body and are different types of force, so they are a balanced pair. The partner of W is the book pulling the Earth upward.
Giving a resultant without a direction
Wrong: The resultant force is −15 N.
Right: The resultant force is 15 N to the left. Force is a vector, so always state its direction in words or as an angle from a stated direction.
Questions students ask
What is the difference between mass and weight in physics?
Mass is the amount of matter in a body and a measure of its inertia; it is a scalar in kilograms and is the same everywhere. Weight is the gravitational force on a body, a vector in newtons acting vertically downward, and it changes with g since W = mg. Mass is measured with a beam balance and weight with a spring balance.
Why are weight and normal force not an action–reaction pair?
Action–reaction partners act on different bodies, are of the same type, and always exist and vanish together. Weight and normal force act on the same body and are different types of force; if the table is removed, N disappears but W remains and the book falls. The partner of the book's weight is the book pulling the Earth upward.
Does a moving object need a resultant force to keep moving?
No. If the resultant force is zero, a moving body continues at constant speed in a straight line. A car cruising at a steady speed has its driving force exactly balanced by friction and air resistance, so forces are needed to change motion, not to keep it going.
How do you find tensions using a closed force triangle?
Choose and state a scale, then draw the known force (usually the weight) to scale and in the correct direction. From its tip and from its start, draw lines parallel to the other two forces; where they cross closes the triangle. Measure the two sides and convert each length to newtons using the scale.
In the full PDF
- •Labelled diagrams, including free-body diagrams of a box on a rough floor, a hanging lamp and a falling skydiver, and the book-on-table action–reaction diagram
- •Further worked examples on weight on the Moon and other planets, collinear and perpendicular resultants, equilibrium, F = ma and a braking car
- •Three scale-drawing worked examples of the closed force triangle, each with a calculation check
- •The remaining common mistakes for every section
- •Comparison tables for contact and non-contact forces, mass versus weight, and balanced versus unbalanced forces
- •End-of-section summaries for quick revision