Mock Exam Review Notes

Accurate: The measured value is close to the true value (small systematic error), but are not necessarily precise

Precise: Repeated measurements have the same value (small random error), but are not necessarily accurate. Precision can be improved by repeating the experiment.

Equilibrium (ΣF = 0): When an object is in equilibrium, the sum of the forces acting on it is zero.

Terminal Velocity: The maximum velocity of a falling object

Newton's Laws of Motion:

1. Unless acted on by an external force, moving objects will remain in uniform motion in a straight line, and objects at rest will stay at rest. External forces cause acceleration.
   
2. Force = mass x acceleration or F = m a
3. For every action, there is an equal but opposite reaction. (Example: If a person pushes against a wall, the wall pushes back with the same amount of force)

Newton's Law of Universal Gravitation:

• Every object in the universe attracts every other object in the universe. This attraction is only significant if the objects involved are massive.
• Universal Gravitational Constant (G) = 6.67 x 10^-11 Nm² kg^-2

Gravitational Field Strength:

• g = F/m
• g = (G M)/r² where M is the mass of the planet
  

Conservation of Momentum: The momentum (p) of a system will remain constant unless the system is acted on by an outside force. Remember: the formula for momentum is p = m v

Escape Speed: The speed needed for an object to escape the gravitational attraction of a planet. Can be found with the formula v = √( (2 G M)/R) where R is the radius of the planet.

Conservation of Energy: Energy is not created or destroyed, it just changes its form

Centripetal Acceleration: a = v²/r

Centripetal Force: F = m a = mv²/r

Celsius to Kelvin Conversion: 0 degrees C = 273 K

Thermal Capacity: The energy required to raise an object's temperature by 1 K

• C = Q/∆T, where C is an object, Q is a quantity of thermal energy, and ∆T is the change in temperature
  

Specific Heat Capacity: The energy required to raise a unit mass of a substance by 1 K

• c = Q/(m∆T)
  

Specific Latent Heat (L): The amount of energy per unit mass absorbed or released during a change of phase

• L = Q/m
• Q = mL

Laws of Thermodynamics:

1. ∆U = ∆Q + ∆W, where ∆U is the change in the internal energy of a system, ∆Q is the thermal energy, and ∆W is the work done. If ∆Q is positive, the thermal energy of the system is increasing. If it is negative, the thermal energy is decreasing. Similarly, if ∆U is positive the internal energy of the system is increasing, and if it is negative the internal energy is decreasing. If ∆W if positive, the system is doing work on its surroundings, while if it is negative the surroundings are doing work on the system.
2. No heat engine can take in heat from its surroundings and convert it totally into work. The entropy of the universe can never decrease.

Ideal Gas Processes:

• Isothermal: the gas has a constant temperature
• Isobaric: the gas has a constant pressure
• Isochoric (isovolumetric): the gas has a constant volume
• Adiabatic: there is no thermal energy transfer between the gas and its surroundings. If the gas does work it must result in a decrease in internal energy.
  

For ideal gases, PV = nRT, where:

• P is pressure
• V is volume
• n is the amount of gas (the units are moles)
• R is the molar gas constant (R = 8.314)
• T is the temperature
  

Simple Harmonic Motion: When an object moves back and forth from a fixed average point (the mean position).

Diffraction: When waves go through openings, they usually spread out. They also spread around obstacles.

Coulomb's Law: F = (k q₁ q₂) / r² where:

• F is the force between two point charges
• k is the Coulomb constant
• q₁ and q₂ are the point charges
• r is the distance between the point charges
  

Mock Exam Review

Notes covering the topics on the mock exam review sheet are on the way!

Hertzsprung Russell Diagram

Pretty good HR Diagram I found online. Click on it to make it bigger.

Class Notes 3/25

Newton's Universe:

1. Infinite size
2. Infinite number of stars
3. Infinite age
4. Homogeneous distribution of stars

H-R Diagram:

• X-Axis: Temperature in K (Note: increases from right to left)
• Y-Axis: Luminosity in Watts
• Main Sequence: made up of dwarf stars (mostly red dwarfs)
• White Dwarfs: below the main sequence, near the lower left corner of the graph
• Cepheid Variables: near the center of the graph, slightly above the main sequence
  

Wolfram Alpha

This website is great for Physics:

www.wolframalpha.com

It seems like you can type in basically any physics concept or formula and it will tell you all about it and answer your math questions. It can do some pretty complicated stuff, and it will convert units if you want it to. I think this could be very helpful.

Class Notes 3/23

Olber's Paradox

1. Newtonian idea of the universe assumes infinite universe and infinite number of stars with homogeneous distribution
2. Number of stars of distance d is about d^2
3. L = b/(4πd^2)

Hubble

1. Discovered galaxies and the enormous number of them
2. The further away a galaxy was the more the Hydrogen spectrum was shifted toward the red.
3. v = H0(d) where H0 is called Hubble's constant
4. (∆λ) / (λref) = v/c
5. The universe is expanding leading to the Big Bang cosmology.
6. Ho = 2.2 x 10^4 m/sMly
7. From v = H0(d) and d = v(avg)T:
   T = d/v(avg) = 1/H0

Schwarzchild Radius:

R = (2GM) / (c^2)

More Astrophysics Notes

What determines the brightness of a star?

• b = L / (4πd²) [W/m²]

What determines the luminosity of a star?

• Assuming a blackbody radiator:

o L = σAT⁴

o σ = 5.67 x 10^-8 [W/m²K⁴]

What determines the surface temperature of a star?

• Wein's Law: T = (2.90 x 10^-3(K·m))/ (λ_max)

More massive stars are also more luminous.

Absolute magnitude (M) is the magnitude of a star when observed from 10 parsecs.

Relative magnitude (m) is the magnitude of a star when observed from the Earth (or nearby).

Stars radiate energy through hydrogen fusion.

F_g = GMm/d²

White dwarf- in equilibrium (not a black hole) due to "electron degeneracy"

1 parsec = 3.26 light-years

Astrophysics Notes

How is the Universe Organized?

· The force of gravity clusters matter at an astronomical scale.

· Clusters within the universe

o Solar Systems consist of: one or more stellar bodies, planets, moons, asteroids, comets, dwarf planets (e.g. Pluto, Eris), Kuiper-belt like debris

o Stellar clusters consist of solar systems

o Galaxies

o Galactic clusters consist of galaxies

· Stars and planets are different because stars emit light while planets reflect light.

· A light-year (ly) is the distance light travels in a year.

· 1 ly = (2.998 x 10⁸ m/s) (3.156 x 10⁷ s/yr) = 9.46 x 10¹⁵ m ≈ 10¹³ km

· Our galaxy is 100,000 ly wide, 2,000 ly tall

· Wein's Law for a blackbody radiator: λ_max = (2.90 x 10^-3) / T (kelvin)

· Gravity bends light

· Andromeda is 2 million ly away