Kinematics and dynamics
Physical quantities and units
What a physical quantity and a unit are, the SI system, prefixes from micro to giga, powers of ten and unit conversions including km/h to m/s. With a calculator.
Scalars and vectors
How a scalar differs from a vector, how vectors are added and multiplied by a number, and how they are resolved into components using sine, cosine and Pythagoras’ theorem.
Motion and rest
Why motion and rest are relative, what a frame of reference, a point particle and a path are, how distance differs from displacement and how motions are classified.
Speed and velocity
What speed is and how it is calculated, average and instantaneous speed, why 60 there and 40 back does not give an average of 50, and why velocity is a vector. With a calculator.
Uniform motion in a straight line
Motion at constant speed along a straight line: the formulae s = v·t and s = s₀ + v·t, why the distance–time graph is a straight line whose steepness is the speed, and how to read the distance from a speed–time graph.
How to solve kinematics and dynamics problems
A step-by-step method for physics problems: writing out the given information, converting units, a sketch, the general solution, checking the units, estimating the result and typical mistakes.
Motion problems
How to solve motion problems: two cars heading towards each other, catching up, a train in a tunnel, and a boat going downstream and upstream. Solving with an equation and with the intersection of graphs.
Acceleration
What acceleration is and why it is measured in m/s². The formula a = Δv/Δt, speeding up and braking, acceleration in a bend using the example of a roundabout, and g-force in multiples of g.
Uniformly accelerated motion
Motion with constant acceleration: the formulas v = v₀ + at and s = v₀t + ½at² from the area under the velocity graph, the distance graph as a parabola, and the relationship v² = v₀² + 2as.
Braking and braking distance
Where a car stops: thinking distance, braking distance and stopping distance. Why twice the speed means four times the braking distance. Calculator.
Free fall
Why a hammer and a feather fall equally fast on the Moon. Free fall with acceleration g, formulas for speed and height, a well, a jump from a tower and a calculator.
Combining motions
How motions combine: walking on an escalator, a boat carried downstream while crossing a river, and rain slanting past a moving car. The principle of independence of motions, with worked calculations.
Uniform circular motion
How to describe motion in a circle: period and frequency, angle in radians, angular velocity and the relation v = ωr. Why the edge of a merry-go-round moves faster than the places near the centre.
Centripetal acceleration
Why a body moving in a circle accelerates even at constant speed. The formula a = v²/r = ω²r, its derivation from a diagram, and examples with a bend, the Earth and a washing machine.
Force
What force is, how much one newton is, and how forces are added and resolved. Resultant force, balanced forces, and why a cable with a lamp on it can never be pulled straight.
Newton’s first law
The law of inertia: why a body with no resultant force stays at rest or moves at a constant velocity in a straight line. A bus, a tablecloth pulled from under the dishes, seat belts and the inertial frame of reference.
Newton’s second law
The law F = m · a: how to work out acceleration from force and mass, and the other way round. Mass as a measure of inertia, the definition of the newton, and why heavy and light objects fall at the same rate.
Newton’s third law
The law of action and reaction: why forces always come in pairs acting on two different objects. The horse and cart paradox, walking, swimming, rockets and a book on a table.
Weight and apparent weight
The difference between mass, weight and apparent weight, the formula for weight, what the bathroom scales show, the normal force, and why we feel heavier in a lift that sets off upwards.
Momentum and impulse
What momentum p = m · v and impulse F · Δt are. Why airbags, crash mats and relaxed hands reduce the force of an impact, and how to write Newton’s second law in terms of momentum.
Conservation of momentum
Why the total momentum of an isolated system does not change. A derivation from Newton’s third law, the recoil of a rifle, two skaters, colliding railway wagons and a rocket.
Friction
Static and kinetic friction, the formula for frictional force and a table of coefficients of friction. Why a wardrobe is harder to get moving than to keep moving, what wheels are for and where the deceleration of a braking car comes from.
Inclined plane
How to resolve the weight on an inclined plane, how large the acceleration of a sledge on a hill is with and without friction, and when a body stays at rest. A worked example step by step.
Centripetal force
What keeps a body on a circle and how large the force is. The formula F = mv²/r, a stone on a string, a car on a bend, the greatest speed for each surface and banked curves.
Fictitious forces
What fictitious and centrifugal forces are, why only someone riding along feels them, and why a description from outside and from inside gives the same result. A train, a lift and a playground roundabout.
Worked examples in kinematics
Thirteen worked examples in kinematics, step by step: distance and displacement, average speed, acceleration, braking distance, free fall, circular motion and reading a graph.
Worked examples in dynamics
Thirteen worked examples in dynamics, step by step: adding forces, Newton’s laws, a lift, momentum and collisions, friction, an inclined plane, a bend and a fictitious force.
