Motion, Forces and Energy

The One Thing

Motion is described quantitatively using distance, displacement, speed, velocity and acceleration, while changes in motion or shape result from forces. Momentum is conserved in closed interactions, and energy is transferred between stores through processes such as work without being created or destroyed.

Reactions, Processes and Experiments

Key Terms

• Distance: The total length of the path travelled by an object; it is a scalar quantity.
• Displacement: The distance travelled in a specified direction from the starting point; it is a vector quantity.
• Speed: The rate at which distance is travelled. speed = distance / time.
• Velocity: The rate of change of displacement in a specified direction. velocity = displacement / time.
• Acceleration: The rate of change of velocity. acceleration = change in velocity / time.
• Scalar: A quantity with magnitude only, such as distance, speed, time, mass and energy.
• Vector: A quantity with both magnitude and direction, such as displacement, velocity, acceleration, force and momentum.
• Resultant force: The single force that has the same effect as all the forces acting together.
• Newton's first law: An object remains at rest or continues at constant velocity unless acted on by a resultant external force.
• Newton's second law: The resultant force on an object equals the rate of change of its momentum; for constant mass, F = ma.
• Newton's third law: When two objects interact, they exert equal and opposite forces on each other.
• Mass: The amount of matter in an object and a measure of its inertia; it is measured in kilograms.
• Weight: The force caused by gravity acting on a mass. weight = mass × gravitational field strength.
• Momentum: The product of mass and velocity. momentum = mass × velocity.
• Impulse: The change in momentum produced by a force acting over a time. impulse = force × time = change in momentum.
• Conservation of momentum: In a closed system with no resultant external force, total momentum before an interaction equals total momentum after it.
• Energy store: A way energy is held in a system, such as kinetic, gravitational, elastic, chemical, thermal or nuclear energy.
• Kinetic energy: Energy stored by a moving object. kinetic energy = 1/2 × mass × speed².
• Gravitational potential energy: Energy stored because of an object's height in a gravitational field. gravitational potential energy = mass × gravitational field strength × height.
• Work done: Energy transferred when a force moves an object through a distance in the direction of the force. work done = force × distance.
• Power: The rate at which work is done or energy is transferred. power = energy transferred / time.
• Efficiency: The useful energy output divided by the total energy input, usually expressed as a percentage.
• Pressure: The force acting normally per unit area. pressure = force / area.
• Liquid pressure: Pressure in a liquid caused by the weight of the liquid above a point. pressure = density × gravitational field strength × depth.
• Density: Mass per unit volume. density = mass / volume.
• Friction: A force that opposes motion or attempted motion between surfaces in contact.
• Drag: A resistive force acting against an object moving through a fluid such as air or water.
• Terminal velocity: The constant maximum velocity reached when resistive forces balance the driving force, giving zero resultant force.
• Moment of a force: The turning effect of a force about a pivot. moment = force × perpendicular distance from the pivot.
• Equilibrium: A state in which the resultant force and resultant moment are both zero.

Easily Confused

• Distance and displacement: Distance is the total path length and is scalar; displacement is the distance from the starting point in a specified direction and is vector.
• Speed and velocity: Speed uses distance and has no direction; velocity uses displacement and has a specified direction.
• Mass and weight: Mass is the amount of matter measured in kilograms; weight is the gravitational force acting on that mass.
• Scalar and vector: Scalars have magnitude only; vectors have magnitude and direction.
• Constant velocity and rest: An object at rest has zero velocity, whereas an object moving at constant velocity is still moving; both have zero acceleration when no resultant force acts.
• Balanced forces and no motion: Balanced forces produce no acceleration, but the object may be stationary or moving at constant velocity.
• Translational and rotational equilibrium: Translational equilibrium requires zero resultant force; rotational equilibrium requires zero resultant moment.
• Friction and drag: Friction acts between surfaces in contact, whereas drag acts against motion through a fluid.
• Work and power: Work is the energy transferred by a force through a distance; power is the rate at which work is done or energy is transferred.
• Momentum and kinetic energy: Momentum is a vector equal to mass × velocity; kinetic energy is a scalar equal to 1/2mv².
• Pressure and force: Pressure is force per unit area, so the same force can produce different pressures when the contact area changes.
• Energy conservation and useful energy: Total energy remains constant, but some energy may be dissipated as thermal energy and become less useful.

What Gets Asked

• Motion calculations: Questions may require average speed, average velocity or acceleration. Marks are lost by using total distance when total displacement is required, or by omitting direction for a vector quantity.
• Constant-acceleration calculations: Questions may require $v=u+at$, $s=ut+1/2a{t}^2$, or $v^2=u^2+2as$. Marks are lost by using an equation without checking which quantities are given.
• Graphs: Questions may ask for the gradient or area of a distance–time, velocity–time or speed–time graph. Marks are lost by confusing the gradient with the area, or by failing to interpret a horizontal section correctly.
• Newton’s laws and free-body diagrams: Questions may ask how force and mass affect acceleration or require relevant forces and direction arrows. Marks are lost by treating a force as necessary for constant velocity or by placing Newton’s third-law forces on the same object.
• Momentum and collisions: Questions may involve conservation of momentum, impulse, airbags, helmets or crumple zones. Marks are lost by ignoring direction when calculating momentum or failing to state that increasing collision time reduces average force for the same change in momentum.
• Energy, pressure and equilibrium: Questions may require work, power, efficiency, pressure, liquid pressure, density or moments. Marks are lost by using area incorrectly in pressure calculations, omitting the perpendicular distance in moment calculations, or confusing equal clockwise and anticlockwise moments with zero force.