OCR A level physics revision notes
Forces and Motion
2. Foundations of physics
Pico Nano Micro Milli Kilo Mega Giga Tera
p n μ m k M G T
× 10−12 × 10−9 × 10−6 × 10−3 × 103 × 106 × 109 × 1012
Scalar quantities have magnitude but not direction. For example: distance, length, mass, speed, temperature, volume,
energy, potential difference, power.
Vector quantities have both magnitude and direction. For example: displacement, velocity, acceleration, force, momentum.
Vectors can represented with lines: the length of the line represents the magnitude of the vector, drawn to scale, and its
direction represents the direction of the vector. Using these lines, vectors can be added:
1. Parallel vectors: add them to find the resultant vector. The direction is the same but the magnitude is greater.
2. Antiparallel vectors: add the vectors, taking into account that the magnitude of one is negative.
3. Perpendicular vectors: draw end-to-end and use Pythagoras’ theorem to find the magnitude of the resultant vector.
Trigonometry can be used to find the direction.
4. Non-perpendicular vectors: construct a vector triangle.
▪ Draw a scale diagram
▪ Use the cosine or sine rule
▪ Resolve one of the vectors into its horizontal and vertical components and combine these with the other vector to
form a perpendicular vector triangle. Then use Pythagoras’ theorem as aforementioned.
Vectors can also be resolved, meaning to split into two perpendicular vectors.
𝐹𝑥 = 𝐹𝑐𝑜𝑠𝜃 and 𝐹𝑦 = 𝐹𝑠𝑖𝑛𝜃
Where θ is the angle made with the x-direction.
3.1 Motion
3.1.1 Kinematics
Definitions:
1. Displacement: a vector quantity that refers to how far an object is from its original position.
2. Instantaneous speed: the speed of a car over a very short period of time, found by drawing the tangent to the distance-
time graph and determining its gradient.
3. Average speed: distance travelled divided by time taken.
4. Velocity: change in displacement divided by time taken.
5. Acceleration: the rate of change of velocity.
Δs Δv
𝑣= and 𝑎 =
Δt Δt
Graphical representations of these quantities:
All these quantities can be represented on graphs (quantity against time).
1. Displacement-time graphs: velocity is gradient.
2. Velocity-time graphs: acceleration is gradient; displacement is area under graph.
3.1.2 Linear motion
There are five SUVAT equations involving motion in a straight line at a constant acceleration.
1. 𝑣 = 𝑢 + 𝑎𝑡
1
2. 𝑠 = (𝑢 + 𝑣)𝑡
2
1
3. 𝑠 = 𝑢𝑡 + 𝑎𝑡 2
2
1
4. 𝑠 = 𝑣𝑡 − 𝑎𝑡 2
2
5. 𝑣 2 = 𝑢2 + 2𝑎𝑠
1
,When an object is accelerating under gravity with no other force acting on it, it is said to be in free fall. The acceleration of
free fall is denoted by g, whose value is 9.81ms-2.
There are various techniques and procedures used to determine the acceleration of free fall:
1. Electromagnet and trap door: an electromagnet holds a small steel ball over a trapdoor. When the current is switched
off, a timer is triggered, the electromagnet demagnetises, and the ball falls. When it hits the trapdoor, the electrical
contact is broken and the timer stops. The value of g is calculated from the height of the fall and the time taken.
2. Light gates: two light gates are attached to a clamp stand, one above the other. These detectors are attached t a timer.
When the ball falls through the first beam, it interrupts the light and the timer start. When it falls through the second
beam (a known distance further down), the timer stops.
3. Taking pictures: a metal ball is dropped from rest next to a metre rule, and its fall is recorded on video or with a
camera in rapid-fire repeating mode. Alternatively, a stroboscope illuminates the scene with rapid flashes, and the
camera shutter is held open to produce a photograph with multiple images of the falling ball.
Car stopping distances:
1. Thinking distance: the distance travelled between the moment when you first see a reason to stop to the moment
when the brake is first applied. Affected by tiredness, intoxication and car speed. The product of speed and reaction
time.
2. Braking distance: the distance travelled from the time the brake is applied to until the vehicle stops. Affected by the
conditions of the brakes, tires, and road, weather conditions and car speed.
3. Stopping distance: the total distance travelled from when the driver first sees a reason to stop to when the vehicle is
stationary. The sum of thinking distance and braking distance.
3.1.3 Projectile motion
The vertical and horizontal motions of a projectile are independent of one another. The vertical velocity changes due to
acceleration of free fall, whereas horizontal velocity remains constant. This means that a projectile has a constant velocity
in one direction and constant acceleration in a perpendicular direction. The only thing unifying the horizontal and vertical
components is the time taken.
The same vector calculations elucidated previously are used for projectile motion.
3.2 Forces in action
3.2.1 Dynamics
Net force is the product of mass and acceleration. The unit of force is newtons (N).
𝐹 = 𝑚 × 𝑎.
The mass of an object is absolute – it is constant for a specific object or particle. However, the magnitude of weight is
variable; it depends on gravitational field strength (location). Weight is the force acting upon an object due to gravity.
𝑊 =𝑚×𝑔
The weight component of an object parallel to the slope is given by 𝑚𝑔sinθ; the component perpendicular to the slope is
given by 𝑚𝑔𝑐𝑜𝑠θ.
Free body diagrams can be used to isolate all the forces acting on a particular object.
Weight The gravitational force acting on an object through its
centre of mass
Friction The force that arises when two surfaces rub against
each other
Drag The resistive force on an object travelling through a
fluid (the same as friction)
Tension The force within a stretched cable or rope
Upthrust An upward buoyancy force acting on an object when it
is in a fluid
Normal contact force A force arising when one object rests against another,
equal to the component of the object’s weight parallel
to the slope.
Each force vector is represented by an arrow labelled with the force it represents; each arrow is drawn to the same scale.
2
,3.2.2 Motion with non-uniform acceleration
Drag is the frictional force experienced by an object travelling through a fluid. Its magnitude depends on several factors,
including the speed of the object, the shape (cross-sectional area) of the object, the roughness or texture of the object, and
the density of the fluid through which it travels. The drag an object experiences when travelling through air is called air
resistance.
Terminal velocity is the maximum velocity that an object falling in a uniform gravitational field can reach, i.e. when its drag
equals its weight.
1. The instant an object starts to fall, there is no drag force on it so the resultant force equals its weight. Therefore, it
accelerates downwards (with an acceleration of g, the acceleration of free fall).
2. As the object falls, its speed increases, and so the opposing drag force increase. This means that the resultant force on
the object decreases and so its instantaneous acceleration decreases (becomes less than g).
3. Eventually the object reaches terminal velocity – the drag force acting upon it equals is equal and opposite to its
weight. There is no resultant force. At terminal velocity, the object has no acceleration so its speed is constant.
You can determine terminal velocity in fluids with light gates/motion sensors. The terminal velocity is reached when the
velocity no longer increases. Using a pulley, the falling object can be attached to a light polystyrene ball by a thin thread;
the light ball’s motion is identical to that of the falling object but easier to measure.
3.2.3 Equilibrium
The moment of a force is the turning effect of a force about some axis or point. It is defined by:
𝑀𝑜𝑚𝑒𝑛𝑡 = 𝑓𝑜𝑟𝑐𝑒 × 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒 𝑜𝑓 𝑎𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑓𝑜𝑟𝑐𝑒 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑝𝑖𝑣𝑜𝑡
𝑀𝑜𝑚𝑒𝑛𝑡 = 𝐹𝑥
The SI unit for the moment of a force is Nm.
The principle of moments states that, when a body is in equilibrium, the net force acting on it is 0 and its net moment is 0.
This means that, for an object in rotational equilibrium, the sum of its anticlockwise moments about any pivot is equal to
the sum of its clockwise moments about the same point.
A couple is a pair of equal and opposite forces applied to an object which act parallel to one another and along different
lines. They make an object spin without translational motion.
The moment of a couple is called a torque. It is defined by the product of one of the forces and the perpendicular
separation between the forces.
𝑇𝑜𝑟𝑞𝑢𝑒 𝑜𝑓 𝑎 𝑐𝑜𝑢𝑝𝑙𝑒 = 𝐹𝑑
The centre of gravity of an object coincides with its centre of mass. This is the point through which any externally applied
force produces straight-line motion but no rotation; it is the point through which the weight of an object appears to act. A
freely suspended object will come to rest with its centre of gravity vertically below the point of suspension. A plumb line
can hence be used to draw multiple lines upon which the centre of gravity always lies: the plumb line will always pass
through the centre of gravity of the object (vertically below the point of suspension), so drawing in the lines delineated by
multiple plumb lines when the card is suspended from different points gives a point of intersection demarcating where the
centre of gravity is.
Three coplanar forces are in equilibrium when a triangle of forces representing them is closed. If drawing three end-to-end
arrows (one for each force) gives a closed triangle, then there is no resultant force so the object is in equilibrium.
3.2.4 Density and pressure
The density of an object is defined as its mass per unit volume.
𝑚
𝜌=
𝑣
Mass is measured directly using a digital balance. Volume is measured either using measurements taken with a ruler,
digital calliper of micrometer (for regular solids), or by displacement (for irregular solids).
Pressure is defined as the normal force exerted per unit cross-sectional area.
𝐹
𝑝=
𝐴
3
, Pressure exists in all fluids due to constant bombardment by molecules. The pressure exerted by a vertical column of
liquid can be calculated by:
𝑝 = ℎ𝜌𝑔
In this equation, h is the height of the liquid column, ρ is the density of the liquid, and g is the acceleration of free fall. The
pressure in any fluid at any particular depth is the same in all directions.
Upthrust is the upward buoyancy force acting on an object when it is in a fluid. It is derived as follows:
𝑓𝑜𝑟𝑐𝑒 𝑎𝑡 𝑡𝑜𝑝 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = ℎ𝜌𝑔𝐴
𝑓𝑜𝑟𝑐𝑒 𝑎𝑡 𝑏𝑜𝑡𝑡𝑜𝑚 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = (ℎ + 𝑥)𝜌𝑔𝐴
𝑟𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝑓𝑜𝑟𝑐𝑒 𝑢𝑝𝑤𝑎𝑟𝑑𝑠 (𝑢𝑝𝑡ℎ𝑟𝑢𝑠𝑡) = (ℎ + 𝑥)𝜌𝑔𝐴 − ℎ𝜌𝑔𝐴 = 𝑥𝜌𝑔𝐴
Archimedes’ principle states that the Upthrust exerted on a body immersed in fluid (fully or partially) is equal to the
weight of fluid displaced. An object will sink if its upthrust is less than its weight, and will float if its upthrust is greater
than its weight.
3.3 Work, energy and power
3.3.1 Work and conservation of energy
Work done is equivalent to the product of the force and the direction moved in the direction of the force.
𝑊 = 𝐹𝑥
Work done has the unit Nm or joule. It is also equivalent to energy transferred (energy is the capacity to do work).
If the force is applied at an angle to the direction at which the object moves, trigonometry is used to find the magnitude of
the force in the direction of movement. This is used to calculate the work done.
The component of the force F in the direction of motion is Fcosθ, so:
𝑊 = 𝐹𝑥𝑐𝑜𝑠𝜃
3.3.2 Kinetic and potential energies
The kinetic energy of an object is given by:
1
𝐸𝑘 = 𝑚𝑣 2
2
The gravitational potential energy of an object in a uniform gravitational field is given by:
𝐸𝑝 = 𝑚𝑔ℎ
When an object falls through a gravitational field, GPE is converted to KE. When it reaches the ground, its GPE is 0 and its
KE is at a maximum.
3.3.3 Power
Power is the rate of work done; its unit is the watt.
𝑊
𝑃=
𝑡
Power is also given by:
𝑃 = 𝐹𝑣
The efficiency of a mechanical system is given by:
𝑢𝑠𝑒𝑓𝑢𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑒𝑛𝑒𝑟𝑔𝑦
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = × 100%
𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑝𝑢𝑡 𝑒𝑛𝑒𝑟𝑔𝑦
3.4 Materials
3.4.1 Springs
A pair of equal and opposite forces is required to alter the shape of an object. Forces that produce an extension (tensile
4
