Dynamics follows on from Kinematics. Kinematics describes motion using speed, velocity and acceleration; Dynamics explains why motion changes. Every time an object speeds up, slows down or changes direction, an unbalanced force is responsible.
These notes cover how to identify the forces acting on an object, draw free-body diagrams, find the resultant force and apply F = ma, identify action–reaction pairs and deal with friction. In Combined Physics you are not asked to state Newton’s laws word for word. You are asked to apply them: given the forces, predict the motion, or given the motion, deduce the resultant force.
What these notes cover
- •What is a force?
- •The four forces you must identify
- •Balanced and unbalanced forces
- •Free-body diagrams: the three-step recipe
- •Three free-body diagrams you must know
- •Resultant force
- •Newton’s second law: F = ma
- •Action–reaction pairs and the four-point rule
- •Friction and its effects on motion
- •Combining kinematics with F = ma
- •Common misconceptions and exam technique
Key definitions
- Force
- A push or a pull acting on an object. It is a vector quantity measured in newtons (N), so both its magnitude and its direction must be given.
- Resultant force
- The single force that has the same effect on a body as all the individual forces acting on it together.
- Free-body diagram
- A diagram of one body drawn on its own, showing only the forces acting on that body. Each force is a labelled arrow starting on the body.
- Action–reaction pair
- Two forces that are equal in magnitude, opposite in direction, of the same type and acting on two different interacting bodies.
- Friction
- A contact force between two surfaces in contact. It acts opposite to the relative motion, or attempted motion, of the object.
Key formulas
Weight
W = mg
W is the weight in N, m is the mass in kg and g = 10 N/kg is the gravitational field strength near the Earth’s surface.
Newton’s second law
F = ma
F is the resultant force in N, m is the mass in kg and a is the acceleration in m/s². The acceleration is in the same direction as the resultant force.
Rearranged forms
a = F ÷ m and m = F ÷ a
For the same resultant force, a larger mass accelerates less. Doubling the mass halves the acceleration.
Resultant force with friction
resultant force = Fd − f
Fd is the forward driving force and f is friction acting backward, taking the direction of motion as positive. If Fd = f, the resultant force is zero and the object moves at constant velocity.
Acceleration from motion data
a = (v − u) ÷ t
u is the initial velocity, v is the final velocity and t is the time taken. Use this to find a first, then substitute it into F = ma.
Definition of the newton
1 N = 1 kg × 1 m/s²
1 N is the resultant force that gives a mass of 1 kg an acceleration of 1 m/s².
Worked example
A box of mass 5.0 kg is pushed along a rough floor with a horizontal force of 24 N. The friction between the box and the floor is 9.0 N. Calculate the acceleration of the box.
- 1Identify the forces: horizontally, the applied force is 24 N forward and friction is 9.0 N backward. Vertically, the weight and the normal contact force are balanced, so they do not affect the horizontal motion.
- 2Taking forward as positive, find the resultant force: resultant force = 24 − 9.0 = 15 N forward.
- 3Apply Newton’s second law to the resultant force: a = resultant force ÷ m = 15 ÷ 5.0 = 3.0 m/s².
- 4State the answer with unit and direction: the acceleration is 3.0 m/s² in the direction of the applied force.
Watch out: Do not substitute the applied force of 24 N into F = ma. F is the resultant force, so write the subtraction line before using the equation.
Common mistakes
Thinking a moving object needs a force to keep moving
Wrong: The trolley is moving at a steady 2 m/s, so a forward resultant force must be keeping it going.
Right: A resultant force is needed to change motion, not to maintain it. An object moving at constant velocity has zero resultant force because all the forces on it are balanced.
Thinking action and reaction cancel out
Wrong: The two forces in an action–reaction pair are equal and opposite, so they cancel and nothing can accelerate.
Right: The two forces act on two different bodies, so they can never cancel. Only forces acting on the same body can be combined into a resultant.
Mixing up mass and weight in F = ma
Wrong: The object weighs 50 N, so use m = 50 in F = ma.
Right: The m in F = ma is the mass in kg. Convert first using W = mg: a weight of 50 N gives m = 50 ÷ 10 = 5.0 kg.
Questions students ask
What is the difference between balanced and unbalanced forces?
When forces are balanced, the resultant force is zero: an object at rest stays at rest and a moving object continues at constant speed in a straight line. When forces are unbalanced, there is a non-zero resultant force, and the object speeds up, slows down or changes direction.
Are weight and normal contact force an action–reaction pair?
No. Weight and the normal contact force both act on the same body, and they are different types of force: weight is gravitational and the normal force is a contact force. The partner of an object’s weight is the object pulling the Earth upward with an equal gravitational force.
How do you draw a free-body diagram?
First isolate the body and draw it on its own as a simple box or dot. Then draw an arrow for every force acting on it, starting on the body: weight always acts, plus one force for each thing the body touches. Finally, label each arrow with its symbol and its value in newtons if known.
What are the ways to reduce friction?
There are three standard methods. Lubricants such as oil or grease separate the surfaces so they do not rub directly, and ball bearings let the surfaces roll instead of slide. Streamlining shapes vehicles smoothly to reduce air resistance.
In the full PDF
- •Labelled force diagrams for a box on a table, a box pulled along a rough floor and an object hanging from a string
- •Further worked examples on car acceleration, braking, constant velocity and a trolley decelerating to rest
- •The three-case friction table and a velocity–time graph for uniform deceleration
- •All six common misconceptions with exam-ready corrections
- •Exam technique habits for explain questions and action–reaction answers
- •A summary at the end of every section