Lewis' Physics Notes

This is a test website for me to learn HTML&CSS and upload physics revision content.It is an ongoing project and will be updated regularly.

AS Physics Content:

Unit 3 - Forces and motion
- Motion
- Forces in action
- Work, energy and power
- Materials
- Newton’s laws of motion and momentum
Unit 4 - Electrons, Waves and Photons
- Charge and current
- Energy, power and resistance
- Electrical circuits
- Waves
- Quantum physics

Click for OCR A-Level Physics Specification

Some of the content on this page goes beyond the A-Level syllabus however it should provide to be useful for understanding the physics.

Unit 3 - Forces and Motion:

Motion:

SUVAT equations and derivations, free fall, displacement-time graphs, velocity-time graphs

Equations of constant acceleration derivation:

Acceleration is the rate of change of velocity with respect to time or
$a=\frac{(v-u)}{t}\Rightarrow v=u+at$
The average velocity is equal to the displacement divided by time or
$\frac{(u+v)}{2}=\frac{s}{t}\Rightarrow s=\frac{1}{2}(u+v)t$
Sub expression for $v$ from i into ii:
$s=\frac{u+(u+at)}{2}t \Rightarrow s=ut+\frac{1}{2}at^{2}$
Sub expression for $t$ from i into ii:
$s=\frac{u+v}{2}(\frac{v-u}{a})=\frac{(v+u)(v-u)}{2a} \Rightarrow v^2=u^2+2as$

Freefall:

An object is in freefall when the only force acting on the object is gravity. For example, a ball that has been dropped. In freefall all objects accelerate at g, $9.81 ms^{-2}$ .

Projectiles:

The first step to solving projectile questions is to resolve the velocity into horizonal and vertical components $v_{x}$ and $v_{y}$ respectively.
The horizontal component of velocity, $v_{x}$ , remains constant due to no horizontal forces acting on the object. This means the equation $v_{x}=\frac{s}{t}$ can be used.

The vertical component , $v_{y}$ , is treated as an object in freefall and thus has an acceleration of g. The equations of constant acceleration can be used for the vertical component.

Motion graphs:

Displacement-Time Graphs:

The gradient of a displacement-time graph is velocity. The steeper the gradient the greater the velocity. A curved graph shows changing velocity - the object is accelerating.

Velocity-Time Graphs:

The gradient of a velocity-time graph is acceleration. The steeper the gradient the greater the acceleration. A curved graph shows changing acceleration - non-uniform acceleration.

Stopping distances:

Stopping distance = Thinking distance + Braking distance
Thinking distance = Distance travelled during the driver's reaction time.
Braking distance = Distance travelled between applying brakes and stopping.
These distances depend on:

Thinking distance:	Stopping distance:
Tiredness	Friction
Alcohol/drugs	Mass
Illness	Braking force

Forces in action:

Forces, acceleration, equilibrium

Forces and acceleration:

Newton's First Law states that "an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted on by an unbalanced (net) force." In other words, an object will not accelerate unless there is a net force acting on the object.

Newton's Second Law states that the rate of change of momentum of a body is directly proportional to the force applied, and this rate of change of momentum takes place in the direction of the applied force.
Represented in mathematical form it looks like this:
$\vec{F}=\frac{\mathrm{d(m\vec{v})} }{\mathrm{d} t} \Rightarrow \vec{F}=m\frac{\mathrm{d\vec{v}} }{\mathrm{d} t}\Rightarrow \vec{F}=m\vec{a}$

Galileo said that all objects fall at the same rate regardless of mass.

Equilibrium:

A force can be resolved into horizontal and vertical components.
$F_{x}=F\cos \theta$
$F_{y}=F\sin \theta$
For an object to be in equilibrium,
$\sum F_{x}=0$ and $\sum F_{y}=0$ .
Pythagoras' theorem is used to find the resultant force:
$|\vec{F}|=\sqrt{\vec{F_{x}}+\vec{F_{y}}}$

Mass, weight and centre of mass:

Mass is the quantity of matter in an object. The greater the mass, the greater the inertia of the object (resistance to changes in motion).
Weight is a force experienced by a mass in a gravitational field.
Weight = mass x gravitational field strength
Centre of mass is the point at which all weight appears to act. This is useful for finding out the stability of an object. If the centre of mass lies outside the object's base area then it will fall over.

Drag and terminal velocity:

Friction is a force that opposes motion. It acts in the opposite direction to the motion of the object. Friction also occurs in fluids such as air or water and is called drag.
Friction increases as speed increases and also depends on surface area.
Terminal velocity is where the driving force is equal and opposite to the drag force.

3 stages to terminal velocity:

Object accelerates with constant driving force.
As velocity increases, resistance force increases. The resultant force decreases so acceleration decreases.
When the driving force = resistance force the resultant force = 0 so the acceleration will be 0. This is terminal velocity.

A common exam question asks about terminal velocity in the context of a skydiver:

A skydiver leaves the plane and accelerates at g.
When the weight force = air resistance he will be travelling at terminal velocity.
The parachute is then opened and the air resistance increases to be greater than the weight so there is deceleration.
When velocity decreases the air resistance decreases until the new terminal velocity is reached.

Density, pressure and upthrust:

Density is mass per unit volume
$\rho = \frac{m}{V}$ .
Density depends on material and not size or shape. The average density determines whether and object will float or sink. If the avergae density is less than the density of the fluid then it will float.
Pressure is the force per unit area
$p = \frac{F}{A}$ .
Pressure due to a fluid depends on depth in fluid, density of fluid and acceleration due to gravity.
$p = h\rho g$ .
When an object is submerged or partically submerged in a fluid there will be difference in pressure from to top to bottom due to a difference in depth. This results in a force called upthrust.
Archimedes' Principle states that upthrust is equal to the weight of the fluid displaced.

Moments and torques:

A moment is the turning effect of a force. The moment of a force = force x perpendicular distance from a pivot.
The principle of moments states that for a body to be in equilibrium, the sum of clockwise moments about any point equals the sum of the anticlockwise moments about the same point.
$\sum clockwise\,moments = \sum anticlockwise\,moments$ .
A couple is a pair of forces of equal size and parallel to each other. There is no resultant linear force but there is a turning force called torque.
Torque of a couple = size of one force x perpendicular distance between forces.

Work, Energy and Power:

Paragraph about energy.

Work and Power:

Work is done when energy is transfered. Work means amount of energy transfered from one form to another when a force causes a movement.
$W=Fx\cos \theta$ .
Power is the rate of work done.
$P=\frac{\mathrm{dW} }{\mathrm{d} t}\, and\, W=\vec{F}\cdot \vec{x} \Rightarrow \, P=\frac{\mathrm{d(\vec{F}\cdot \vec{x})} }{\mathrm{d} t} \Rightarrow P=\vec{F}\cdot \frac{\mathrm{d\vec{x}} }{\mathrm{d} t} \Rightarrow P=\vec{F}\cdot \vec{v}$ .

Conservation of Energy and Efficiency:

Kinetic energy is energy an object has due to movement.
$E_{k}=Fx\, ,F=ma\, ,a=\frac{(v-u)}{t}\, ,x=\frac{(u+v)}{2}t\Rightarrow E_{k}=max\Rightarrow E_{k}=m(\frac{v-u}{t})(\frac{u+v}{2})t\Rightarrow E_{k}=\frac{1}{2}mv^{2}-\frac{1}{2}mu^{2}, u=0\Rightarrow E_{k}=\frac{1}{2}mv^{2}$ .
Gravitational potential energy is energy an object has due to its position in a gravitiational field.
$E_{p}=W=Fh \Rightarrow E_{p}=mgh$ .
The principle of conservation of energy states that "Energy cannot be created or destroyed. Energy can be transferred from one form to another but the total energy in a closed system will not change."
Energy is often wasted in the form of heat.
$Efficiency=\frac{useful\, output\, energy}{total\, input\, energy}\cdot 100$ .

Materials:

Hooke's law, Stress, Strain and energy.

Hooke's Law:

Hooke's law says the force exerted on a mass, permanently or temporarily attached to the spring, is proportional to the difference between the instantaneous length of the spring and the equilibrium length. In the direction which points toward the equilibrium.
$F=kx$ .
The direction of extension is opposite to the direction of force so in vector form the equation becomes
$\vec{F}=-k\vec{x}$ .
Hooke's law applies up to the limit of proportionality which is the the point at which up to it the relationship between force and extension is linear.

For springs in series or parallel the individual spring constants, $k_{a}$ and $k_{b}$ , can be combined to find the equivalent spring constant.
In series:
$\frac{1}{k_{eq}}=\frac{1}{k_{a}}+\frac{1}{k_{b}}$ .
In parallel:
$k_{eq}=k_{a}+k_{b}$ .

Elastic deformation: Up to the elastic limit, a material will return to its original length when forces are removed.
Plastic deformation: This occurs beyond the elastic limit and when forces are removed, the material does not return to its original shape.

Stress, strain and elastic potential energy:

When a material is stretched by a pair of opposite forces, the forces are tensile. When compressed by a pair of opposite forces, the forces are compressive.
Tensile stress:
$\sigma = \frac{F}{A}$
Tensile strain:
$\varepsilon =\frac{x}{l}$

The ultimate tensile stress is the maximum stress a material can take. ( I will add a graph when I figure out how).

The Young Modulus:

The Young Modulus applies to materials, not objects so is not affected by size.
Young's Modulus is a measure of how much stress is required to produce a given strain. A large Young's Modulus means a large stress is required to produce a small strain meaning the material does not deform easily.

$E=\frac{\sigma }{\varepsilon }$

Up to the limit of proportionality, $\sigma \propto \varepsilon$ .

On a stress-strain graph, the gradient is equal to the Young Modulus.
The area is equal to the elastic potential energy per unit volume.

$E_{ep}=\frac{1}{2}\sigma\cdot \varepsilon$

Newton's Laws of Motion and Momentum:

Momentum, Impulse and Newton's Laws of Motion

Momentum and Impluse:

$\vec{p}=m\cdot \vec{v}$

The Principle of Conservation of Momentum states that in a closed system, the initial total momentum is equal to the final total momentum.
In 2-dimensional collisions momentum is conserved in both dimensions.

Newton's Experimental Law tells us the coefficient of restitution, $e$ , in a collision.

$-e(u_{1}-u_{2})=v_{1}-v_{2}$

When $e=1$ , the collision is perfectly elastic where momentum and kinetic energy is conserved.
When $e=0$ , the collision is perfectly inelastic where no kinetic energy is not conserved and instead is dissipated to other forms such as heat.
When $0< e< 1$ , the collision is inelastic where some kinetic energy is dissipated.

Impluse is a change in momentum. It is the integral of a force over the time period for which it acts.

$\vec{I}=\int \vec{F}dt$

$\vec{I}=\Delta \vec{p}$

Newton's Laws of Motion:

Newton's First Law of Motion states that the velocity of an object will not change unless a net force acts on it.

Newton's Second Law of Motion states that "the rate of change of momentum of an object is directly proportional to the net force which acts on the object.

Newton's Third Law of Motion states that if object A exerts a force on object B, then object B exerts an equal but opposite force of object A.
An example of this is when you throw a ball at a wall the ball exerts a force on the wall and the wall exerts an equal but opposite force on the ball.
This is due to the conservation of momentum.

Unit 4 - Electrons, Waves and Photons:

Charge, Current and Potential Difference:

Current is the rate of flow of charge.

$I=\frac{\mathrm{dQ} }{\mathrm{d} t}$

A coulomb is the amount of charge that passes in 1 second when the current is 1A.

The charge on an electron is the smallest unit of charge.
$e=-1.60\cdot 10^{-19}C$
It is a quantised value so the net charge will always be a multiple of $e$ .

Potential Difference is the work done per unit charge.

$W=VQ$

The volt is defined as $1V=1JC^{-1}$ .

When a charged particle is accelerated by a potential difference, the energy transfered to it is equal to the work done on the particle. For an electron, $W=eV$ . This is equal to the kinetic energy of that particle.
$eV=\frac{1}{2}mv^{2}$ .

The mean drift velocity of charge carriers is simply the average velocity. $I=Anev$ .

Resistance and Resistivity

Electrical resistance of a conductor is a measure of the difficulty to pass a current through that conductor.

Ohm's Law states that given a constant temperature, the current through and ohmic conductor is directly proportional to the potential difference across it.
$I=\frac{V}{R} \Rightarrow R=\frac{V}{I}$

Resistivity is a property of a material and is the resistance of a 1m length with a 1m^2 area. It is a measure of a material's ability to oppose electric current.

$\rho =\frac{R L}{A}$

Resistivity of a metal increases with temperature. When temperature is increased, the ions vibrate more resulting in more collisions between electrons and ions.

Semiconductors have a higher resistivity due to fewer charge carriers. Resistivity of semiconductors decreases when energy is supplied e.g. through heat or light. This is due to charge carriers being released.

In a thermistor, resistance decreases as temperature increases. In an LDR, resistance decreases as light intensity increases. This is due to increased energy allowing electrons to escape from their atoms. Increased number of charge carriers = lower resistance.

Electrical energy and Power

Electric power is the rate per unit time at which electrical energy is transfered by and electric circuit.

$P=\frac{VQ}{t}=VI$

Joule's law states that the heat produced by an electric current, I, flowing through a resistance, R, for a time, t, is proportional to $I^{2}Rt$

$P\propto I^{2}Rt$

Ohm's law states that $V=IR$

$P=IV=I^{2}R=\frac{V^{2}}{R}$

E.M.F. and Internal Resistance:

Batteries have an internal resistance. Chemical energy makes electrons move which collide with atoms in the battery.

Potential Difference is energy converted per unit charge from electrical energy to other forms of energy in a load.

Electromotive Force, E.M.F., is energy converted per unit charge to electrical energy from other forms of energy in a source.

$W=VQ\: and\: W=\varepsilon Q$

$\varepsilon =V + v$

In series: $\varepsilon _{total}=\sum \varepsilon$
In parallel: $\varepsilon _{total}=\varepsilon _{1}=\varepsilon _{2}=\varepsilon _{n}$