SAT II Physics

Syllabus (as set by the College Board)

CONTENT Approximate % of Test

Level of Concept Application

Recall (20–33%)

Single-Concept Problem (40–53%)

Multiple-Concept Problem (20–33%)

The purpose of this 'book' is to provide quick revision to students. It is by no means a replacement for a typical school textbook. All the topics in the syllabus are covered. For detailed information, click the hyperlinks which will take you to the relevant topics in wikipedia.

Mechanics (36–42%)

A. Kinematics includes velocity, acceleration, motion in one dimension, and motion of projectiles.

B. Dynamics includes force, Newton’s laws, and statics.

C. Energy and Momentum includes potential and kinetic energy, work, power, impulse, and conservation laws.

D. Circular Motion includes uniform circular motion and centripetal force.

E. Simple Harmonic Motion includes mass on a spring and the pendulum.

F. Gravity includes the law of gravitation, orbits, and Kepler’s laws.

9.===Kinematics===

Distance

Distance is defined as the entire distance traveled by an object.

Displacement

Displacement is the distance covered in a particular direction or rather, it is the overall change in position. Distance is a scalar quantity, but displacement is a vector.

Velocity

Velocity is defined as the rate of change of displacement. It is speed in a particular direction. Speed is a scalar while velocity is a vector.

It is crucial to remember that only displacement is used in to calculate velocity and not distance. Thus, if an object goes in a circle and returns to its initial point, the displacement is 0 and the velocity is therefore 0 m/s as 0 m/s is always equal to zero. Even if the object is moving a speed of 100 m/s when making that one loop, the lack of a displacement means that the velocity is 0.

Formula: v = d/t

where

v = velocity d = displacement t = time

Acceleration

Acceleration is the rate of change of velocity. Acceleration is said to take place when either the speed of an object changes, or its direction changes.

When the acceleration and the velocity of an object are in the same direction, an object is speeding up. When the acceleration and the velocity of an object are in opposite directions, an object is slowing down or decelerating. This can be explained as the acceleration being negative relative to the velocity which means that the acceleration would actually be deceleration relative to the velocity we know as the act of slowing down. When the acceleration and the velocity of an object are perpendicular to each other, the object is turning.

Formula: a = Δv/t

where

a = acceleration Δd = displacement t = time

Kinematics Formulas

v² - u² = 2ad

d = ut + 1/2 at²

d = vt - 1/2 at²

v = u + at

d = 1/2 (u + v)t

where

d = displacement u = initial velocity v = velocity t = time a = acceleration

Graphs of Kinematics

Position vs. Time Graphs

The slope of a position vs. time graph is the equal to the velocity

The area inside the graph of a velocity vs. time graph is equal to the displacement

Projectile Motion

When solving projectile motion questions, the question can be broken up into horizontal motion and vertical motion components that are independent

Horizontal Motion

Horizontal motion is unaffected by the acceleration caused by gravity and the initial horizontal velocity is constant throughout the entire motion with the absence of air resistance.

The horizontal distance traveled by a projectile can be calculated with the initial horizontal velocity and the projectile's air time.

Vertical Motion

Vertical Motion is affected by the acceleration due to gravity or g which is equal to 9.81 m/s² which can also be rounded to 10 m/s² as the SAT II does not allow the use of calculators and simple numbers will make calculations easier.

With projectile motion, the vertical motion can simply be treated as the motion of a projectile being thrown straight up then falling back down as the horizontal component does not affect the vertical motion.

The total air time of a projectile can be calculated with the following formula.

Formulas: t = 2u/g

where

t = air time u = initial vertical velocity g = acceleration due to gravity

Dynamics

Newton's Laws

1. An object continues in its state of rest or uniform motion, until an external force is applied to it.

This law is called the law of inertia. Inertia is an object's resistance to motion and is directly proportional to the mass of said object.

2. The rate of change of momentum is proportional to the applied force and takes place in the direction of the force.

Formula: F = ma

where

F = net force in Newtons

m = mass

a = acceleration

3. Every action has an equal and opposite reaction.

Law of Gravitation

Is the attractive force exerted by two objects.

Formula: F = Gm1m2/r²

where

F = force of gravity in Newtons

m1 = mass of object 1

m2 = mass of object 2

G = Universal Gravitational Constant (6.67 * 10^-11 Nm²/kg²)

m1a1=m2a2 or F1=F2 because the force exert by two objects on eacch other will be equal by in opposite directions.

Other Definitions:

Weight

Is the force that gravity exerts on an object.

Formula: w=mg

where

w = weight

m = mass

g = acceleration due to gravity

Potential Energy

Is the energy possessed by a body due to its position in a gravitational field.

Formula: E = mgh

where

E = potential energy

m = mass of object

g = gravity (ie 9.8 ms²)

h = height above the ground

Kinetic Energy

Is the energy possessed by a body due to its motion.

Formula: E = 1/2 mv²

where

E = kinetic energy

m = mass of the moving body

v = velocity of the body

Momentum

Is the product of the mass and velocity of a body.

Formula: p = mv

where

p = momentum in Ns or kgms^-1

m = mass

v = velocity

Power

Is the rate at which work is done.

Formula: Power = Work/Time

Impulse

Impulse is a force acting for a very short period of time, as during in a collision.

Formula: Force = Change in Momentum/Time = Mass x Acceleration

and

Impulse = Force x Time = Change in Momentum = Mass x Change in Velocity

Simple Harmonic Motion:

Fs=-Kx

where

F = force of spring K = constant of spring s = displacement

Electricity and Magnetism (18–24%)

A. Electric Fields, Forces, and Potentials, such as Coulomb’s law, induced charge, field and potential of groups of point charges, and charged particles in electric fields.

Coulomb's Law $F=k{\frac {q_{1}q_{2}}{r^{2}}}$ , where $F$ is the magnitude of the electrostatic force, $q_{1}$ and $q_{2}$ are the charges of individual particles, $r$ is the distance between the two particles, and $k$ is the Coulomb's constant. In a vacuum, this is $k_{0}\approx 8.99\times 10^{9}{\frac {Nm^{2}}{C^{2}}}$ , and can also be expressed as $k_{0}={\frac {1}{4\pi \varepsilon _{0}}}$ , where $\varepsilon _{0}\approx 8.85\times 10^{-12}{\frac {C^{2}}{Nm^{2}}}$ is the permitivity of free space.

B. Capacitance, such as parallel-plate capacitors and transients.

C. Circuit Elements and DC Circuits, such as resistors, light bulbs, series and parallel networks, Ohm’s law, and Joule’s law.

D. Magnetism, such as permanent magnets, fields caused by currents, particles in magnetic fields, Faraday’s law, Lenz’s law.

Waves and Optics (15–19%)

A. General Wave Properties, such as wave speed, frequency, wavelength,superposition, standing waves, and Doppler effect.

B. Reflection and Refraction, such as Snell’s law and changes in wavelength and speed.

C. Ray Optics, such as image formation using pinholes, mirrors, and lenses.

D. Physical Optics, such as single-slit diffraction, double-slit interference, polarization, and color.

Heat and Thermodynamics (6–11%)

A. Thermal Properties, such as temperature, heat transfer, specific and latent heats, and thermal expansion.

B. Laws of Thermodynamics, such as first and second laws, internal energy, entropy, and heat engine efficiency.

Heat

Heat, or thermal energy, always flows from a region of higher temperature to a region of lower temperature.

When two bodies are in thermal equilibrium, no net heat flows between them.

Methods of Heat Transfer

Conduction

Method of heat transfer without appreciable motion of the medium. 'Free electrons' conduct the heat.

As metals have a lot of free electrons, they are very good conductors of heat.

Air, glass, water, and vacuum are bad conductors (or good insulators) of heat.

Convection

Heat transfer in fluids due to the motion of fluids themselves.

Also see convection currents.

Radiation

Heat transfer due to wave motion.

Black surfaces are good radiators and good absorbers of heat.

White and shiny surfaces are bad radiators and absorbers of heat.

Radiation, unlike conduction and convection, can also take place in a vacuum.

Specific and Latent Heat

Specific Heat Capacity

Is the amount of heat required by one kilogram of a substance to raise its temperature by one kelvin.

Formula: E = mcΔθ(formulae given by the great scientist Mehar who is still alive and young)

where

E: energy

m: mass

c: specific heat capacity

Δθ: change in temperature

Specific Latent Heat

Is the amount of heat required to bring about a change in state of a kilogram of a particular substance, without changing the temperature of the substance. (For example, changing a kilogram of ice to water at 0°C.)

Formula: E = ml

where

E: energy

m: mass

l: specific latent heat

See also latent heat of fusion and latent heat of vaporisation.

Laws of Thermodynamics

First Law of Thermodynamics

The total energy of a closed system is conserved.

Formula: Q = ΔU + W

where

Q: heat transferred to system

ΔU: change in internal energy

W: work done by the system

The first law of thermodynamics is also called the law of conservation of energy.

Internal Energy

Is the total of the microscopic kinetic and potential energies of the molecules in a substance.

Second Law of Thermodynamics

Heat cannot flow from a cooler region to a hotter region unless external work is done.

Miscellaneous Definitions

Entropy

Entropy is a measure of the random disorder of a system. The higher the entropy, the more disordered the system

Formula: Entropy = Heat Absorbed/Kelvin Temperature

The entropy (not the energy) of the Universe is increasing.

Thermodynamic Temperature

Temperature which is measured in kelvins.

Kelvin = Celcius + 273°

0°K is called the absolute zero.

273°K is the freezing point of water.

373°K is the boiling point of water.

Heat Engine Efficiency

Efficiency of a system = Work done by the system / Energy supplied to the system.

The efficiency of diesel engines(about 40%) is usually more than gasoline or steam engines.

Modern Physics (6–11%)

A. Quantum Phenomena, such as photons and photoelectric effect.

B. Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra.

C. Nuclear and Particle Physics, such as radioactivity, nuclear reactions, and fundamental particles.

D. Relativity, such as time dilation, length contraction, and mass-energy equivalence.

Miscellaneous (4–9%)

A. General, such as history of physics and general questions that overlap several major topics.

B. Analytical Skills, such as graphical analysis, measurement, and math skills.

C. Contemporary Physics, such as astrophysics, superconductivity, and chaos theory.

Laboratory Skills: In each of the six major topics above, some questions may deal with laboratory skills in context.