IB Physics HL

Fundamental SI units

kilogram (kg), metre (m), second (s), ampere (amp), mole (mol), kelvin (K)

Random error

An unpredictable and largely uncontrollable uncertainty. (Examples include human reaction time and other forms of human measurement.) (Random errors can be reduced by taking the average of repeated measurements.)

Systematic error

An error that occurs on all measurements. (An example is a zero error on a scale.) (Systematic errors can NOT be reduced by repeated measurement.)

Vectors

displacement, velocity, acceleration, force, momentum.

Scalars

mass, length, speed, energy, time.

Displacement

the position of an object relative to a defined starting position

Velocity

the rate at which displacement changes (with time)

Speed

the rate at which distance changes (with time)

Acceleration

the rate at which velocity changes (with time)

Instantaneous speed

the speed at a particular moment in time

Average speed

the total distance travelled divided by the total time taken (the average rate of movement)

Equations of uniformly accelerated motion

v = u + at
s = ½(u+v)t
s = ut + ½ at²
v² = u² + 2as

Newton's First Law

A body will continue in its current state of motion (velocity) unless acted upon by a resultant force
(a = 0 if ∑F = 0)

Newton's Second Law

The acceleration of a body is proportional to the resultant force acting on the body (and is in the same direction)
∑F=ma ∑F= Δp/Δt

Newton's Third Law

When two bodies interact, the force that body 1 exerts on body 2 is equal and opposite to the force that 2 exerts on 1
(F ₁₂= -F ₂₁)

Inertial mass

The mass of a body as determined by the second law of motion from the acceleration of the body when it is subjected to a force that is not due to gravity. (The measurement of an object's resistance to changes of motion)

Gravitational mass

The mass of a body as measured by its gravitational attraction for other bodies.

Linear momentum

A quantity associated with the motion of an object along a straight path. The linear momentum of an object is defined to be equal to its mass times its velocity.

Impulse

The change in momentum. (Impulse is the integral of force over time) (Impulse therefore is the area under a force-time graph)

Work

The amount of energy transferred by a force acting through a distance

Kinetic Energy

The mechanical energy that a body has by virtue of its motion.

Gravitational Potential Energy

The energy gained by an object as its height above ground level increases.

Conservation of energy

Energy is never gained or lost, it is merely transferred from one form to another.

Power

The rate at which work is performed or energy is converted.

Efficiency

A measure of the effectiveness with which a system performs. (useful work done/total energy used) x 100

Centripetal acceleration

a = v²/r

Projectile motion

An object moving with projectile motion is moving horizontally and vertically at the same time but the horizontal and vertical components of the motion are independent of one another. (this is true when the gravitational force is always constant)

Horizontal component of projectile motion

The horizontal velocity is constant as there is no force and therefore no acceleration in the horizontal direction.

Vertical component of projectile motion

There is a constant vertical force and therefore a constant vertical acceleration. The value of this is the value of the acceleration due to gravity.

Newton's law of gravitation

Any two bodies attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
F= G(m₁x m₂/ r²)

Gravitational Field Strength

(at a point in a gravitational field) it is the force acting on a 1kg mass placed at that point

Gravitational Potential Energy

(of a mass) the energy required (work done) to move it from infinity to its position in the field.

Gravitational Potential

(of a position) the work done per unit mass in bringing a test mass from infinity to that position in the field.

Kepler's Third Law

The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
(T² α R³) and T²/R³ = constant

G.P.E and K.E of satellites.

K.E - ½mv² but v = √(GM)/r ∴ KE = ½ m (GM)/r = ½ (GMm)/r
G.P.E = -(GMm)/r
(the K.E is half the magnitude of the G.P.E when in orbit)
Total energy = KE + GPE = ½ (GMm)/r -(GMm)/r = -½ (GMm)/r

Temperature

A measure of the average kinetic energy of molecules in a substance.

Heat

A form of energy that is transferred by a difference in temperature.
(When two objects are in thermal contact, energy will be transferred in the direction hot -> cold)

Relationship between Celsius and Kelvin

°C -> K = + 273
K -> °C = - 273
0K = -273°C = absolute zero

Internal energy

(symbol U) the energy held within a system. The sum of the PE due to the intermolecular forces and the KE due to the random motion of the molecules. A change in temperature or phase results in a change in internal energy.

Ways energy is transferred

Radiation, Conduction, Convection and Work

Heat Capacity

The energy required to raise an objects temperature by 1K
Q=cΔT

Specific Heat Capacity

The energy required to raise a unit mass of substance by 1K
Q=mcΔT

Specific Latent Heat

The amount of energy per unit mass absorbed or released during a change of phase. Q= mL

Gas laws

At a constant V, PαT - Pressure law
At a constant P, VαT - Charles' Law
At a constant T, P α(1/V) - Boyles Law

Mole

The basic SI unit for amount of substance. One mole is equal to the amount of the substance that contains the same number of atoms as 0.012 kg of Carbon-12.

Molar mass

The mass of one mole of a substance. If an element has mass number 'A' then the molar mass will be A grams.

Avogadro's constant

The number of atoms in 0.012kg of Carbon-12. (It is 6.02x10²³)

Ideal gas equation

PV=nRT where P = pressure, V= volume, n = number of moles, R = the molar gas constant and T = temperature.

0th Law of Thermodynamics

If two systems are in thermodynamic equilibrium with a third system, then they are in thermal equilibrium with each other.

1st Law of Thermodynamics

If an amount of thermal energy is given to a system then one of two things must happen: the system can increase its internal energy or it can do work.
ΔQ = ΔU + ΔW

Thermal efficiency

The ratio of useable heat energy output to energy input.
Heat Engines = (work done / thermal energy taken from hot reservoir) or (rate of doing work / thermal power taken from hot reservoir).
Carnot Engine = 1-(T cold/T hot) ( T is in Kelvin)

Carnot's theorem.

All irreversible heat engines between two heat reservoirs are less efficient than a Carnot engine operating between the same reservoirs.
All reversible heat engines between two heat reservoirs are equally efficient with a Carnot engine operating between the same reservoirs.

Kelvin Planck statement of the 2nd Law

No heat engine, operating in a cycle, can take in heat from its surroundings and totally convert it into work.

Clausius statement of the 2nd Law

No heat pump can transfer thermal energy from a low-temperature reservoir to a high-temperature reservoir without work being done on it.

Entropy

A property that expresses the disorder in a system.
Entropy change ΔS = ΔQ/T
Entropy decrease = ΔQ/T(hot)
Entropy increase = ΔQ/T(cold)

2nd Law in terms of entropy

The entropy of the universe can never decrease.

What waves transfer

Energy

Displacement

Instantaneous distance of a moving object from its mean position in a specified direction

Amplitude

Maximum displacement from mean position

Period

Time taken for one complete oscillation (T = 1/f)

Frequency

Number of oscillations completed per unit time

Wavelength

distance along the axis of a wave from one part to the next occurence of this part (e.g one crest to another) (λ)

Wave speed

The speed in which the wave fronts pass a stationary observer

Huygen's principle

The principle that any point on a wave front of light may be regarded as the source of secondary waves and that the surface that is tangent to the secondary waves can be used to determine the future position of the wave front.

Principle of superposition of waves

The overall disturbance at any point and at any time where the waves meet is the vector sum of the disturbances that would have been produced by the individual waves.

Snell's Law

The ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media, or equivalent to the opposite ratio of the indices of refraction.

Conditions for interference (between 2 light sources)

The light sources must be coherent, monochromatic and have the same amplitude.

Types of electric charge

Positive and Negative

Coulomb's Law

The magnitude of the electrostatic force of interaction between two point charges is directly proportional to the multiplication of the magnitudes of charges and inversely proportional to the square of the distances between them.
F= k (q₁q₂/ r²)

Electric field

A region of space characterized by the existence of a force generated by electric charge.

Potential difference

The energy difference per unit charge

Electronvolt

A unit of energy equal to the work done by an electron accelerated through a potential difference of 1 volt

Electric current

The rate of flow of electrical charge.

Resistance

The mathematical ratio between potential difference and current.

Ohm's Law

The current flowing through a piece of metal is proportional to the potential difference across it (providing the temperature remains constant). V ∝ I (if temp is constant)

Volt

One volt is the force required to send one ampere of electrical current through a resistance of one ohm.
it is also equal to one joule of work per coulomb of charge transferred.

Magnetic Field Strength

the force per unit length per unit current on a current carrying conductor at right angles to the field lines.

Ampere

(SI Unit of electric current) one ampere is the flow of one coulomb of charge per second

Electric potential

(at a point) V = W/q where W = the work done bringing a positive test charge (q) from infinity to that point in the electric field.
for a single point charge V = Q/4πε₀r

Electric potential energy

the energy that a charge has as a result of its position in an electric field.
(change in electric potential energy = Force x distance = E q x d)

Electric field strength and potential gradient

Moving a positive charge through an electric field requires work to be done against the electrostatic force. The work done δW = - E q δx ( the negative sign is needed because the direction of the force required to do work is in the opposite direction to E)
E = - δV/δx (as δV = δW/q)
therefore electric field strength = - potential gradient

Magnetic Flux

A measure of the amount of field lines passng through an area, at right angles to the area.
Φ = BA cosθ

Magnetic Flux Linkage

a measure of the number of turns of wire 'linked to' (passing through) magnetic flux = Φ x N = flux x number of turns

Faraday's Law

the induced emf in a circuit is equal to the rate of change of flux linkage through the circuit

Lenz's Law

the direction of the induced current (or emf) is always so as to oppose the charge causing it

Root mean square voltage

The RMS value is the effective value of a varying voltage. It is the equivalent steady DC (constant) value which gives the same effect.
Vrms = Vpeak / √2

Root mean square current

The RMS value is the effective value of a varying current. It is the equivalent steady DC (constant) value which gives the same effect.
Irms = Ipeak / √2

Mass number

Number of protons and neutrons in the nucleus. (Different for dfferent isotopes)

Atomic number

Number of protons in a nucleus.

Half life

The time taken for half of the nuclei in a sample to decay

Unified mass unit

exactly one twelfth of the mass of a carbon-12 atom

Radioactive decay law

As the rate of decay of a sample is proportional to the number of atoms in the sample: radioactive decay is an exponential process. dN/dt α - N
Also, N = N₀ e^ -λt where N₀ = number of radioactive nuclei present initially.

Decay constant

the probability of a nucleus decaying in a second

Fundamental particles

Leptons, Quarks and Exchange Bosons

Observed particles

Leptons, Hadrons and Exchange Bosons

Light year

that light travels in a vacuum in 1 year

Main energy source of stars (including the sun)

nuclear fusion

Stable star equilibrium

Stable stars are stable because there is an equilibrium between the outward radiating pressure and the inward gravitational force.

Luminosity

The total amount of energy emitted by the star per second.

Apparent brightness

The power received per unit area. It is measured by the equation b=L/4πd².