Gravity

• On the earth's surface g (acceleration due to gravity) is approximately 9.8m/s^2 (((6.67*10^-11)(5.98*10^24)) / (6.4 * 10^6)^2)....go on, calculate it and see for yourself..!
  
  
• but when the object is WAAAAY above the earth's surface, g = GM / R^2
  and one can infer that... GM = g(1)R(1)^2 = g(2)R(2)^2

Kepler's Laws

• Some scientist named Kepler was the first person to look for physical laws based on measureable phenomenoa to describe the universe. Until then, it was thought that spirits were responsible for the motion of objects. So, he formulated 3 laws...
  
  
  • The paths of the planets around the sun are elliptical
  • The planets sweep equal areas around the sun in equal intervals of time
  • For any planet, the ratio of the cube of their mean radius and the square of their period is a constant.
    ie R^3 / T^2 = K

Satellites and Weightlessness

• people in a space shuttle are not weightless (g = [approx] 8.4m/s^2)...but they are in an environment of relative weightlessness
  ie both the shuttle and the astronauts are falling to the earth at the same rate (see the elevator analogy on P.112 if you like pictures instead of words)
• they are weightless with respect to each other
• if it stopped, it would fall towards the earth and start accelerating at 8.4m/s^2 (assuming an altitude of 500km)
• if it is travelling too fast, it would escape the earth's gravitational field, never to return
• assume satellites move in circular orbits
• centripetal acceleration is supplied by gravity...thus a(c) = a(g)

Electrostatics

• there are two types of charges: like and unlike, or in lamen's terms, positive and negative
• unlike charges attract, like charges repel
• "charged" objects have a net charge...that is, they have more positively particles than negatively charged particles, or vice versa
• neutral objects contain both positively and negatively charged particles, both of which are equal in number
• charged objects often attract neutral objects - why? say an positively object is brought near a neutral object, the positively charged particles (from the charged object) is attracted to the negatively charged particles (from the neutral object) and thus, the two objects attract each other...

Coulomb's Law

• defines the force between point charges
  

  F =	kQq ----- R^2

  
  
• where k is Coulomb's constant of 9.0 * 10^9 Nm^2/C^2
• Q and q are the point charges measured in coulombs
• and R is the distance between the points

Electric Fields

• the electric force described by Coulomb extends in space to create the electric field invented by Faraday
• the direction of the field is the direction in which a positive point charge would move when placed around a charge
• the electric field between two parallel plates is constant
• the electric field inside a conductor is zero
• the electric field outside a conductor is perpendicular to the surface area
• the field strength, E, is defined as the force exerted on a small test charge, q, placed in the field
  

  E =

  F -- q

  =>

  (kQq)/r ---------- q

  =>

  E =

  kQ ---- r^2

• measured in N/C
  The Superposition Principle
• when the field is due to more than one charge, the individual fields are added together according to the rule of vector addition
  

Electric Potential

• at infinity, the electric potential between two charges is zero
• as q approaches Q, the electric potential increases and the force between them increases
  

• the potential energy between like charges is positive because you do work on them by forcing them together
• the electric potential between unlike charges is negative because you do not do work to bring them together
  electric potential

  Ue =	kQq ----- r

  
  
• the voltage on q at r is the potential per unit charge

Vt = kQ1/r1 + kQ2/r2...
+q = positive potential
-q = negative potential

• Voltage is work per charge (J/C)
• the field is uniform
• the force required to move a charge from the positive plate to the negative plate is F = Eq (remember, E=kQ/r^2)
• if the plates are a distance d apart, the work done to move a charge is Fd = Eqd
• one electron volt (eV) is the energy acquired by an electron moving through one potential difference of one volt

Current

• current is the rate of flow of charge
• measured in Coulombs per second.....so, 1A = 1C/s
• flows from positive to negative
• electron flow goes from negative to positive

Voltage

• voltage is energy per charge
• measured in Joules per Coulomb......so, 1V = 1J/C

Resistance

• Ohm's Law defines resistance in terms of voltage and current
• V = IR
• resistance is measured in ohms.....so, 1 ohm = 1V/A

Series Circuits

• Current is same through each resistor...that is I(t) = I(1) = I(2) = I(3)...
• Voltage is completely used up by each of the resistors... that is V(t) = V(1) + V(2) + V(3)...
• Resistance is the sum of resistances from all the resistors... that is R(t) = R(1) + R(2) + R(3)...
  

Parallel Circuits

• Current is the sum of the currents at each resistor... that is I(t) = I(1) + I(2) + I(3)...
• Voltage stays the same... that is V(t) = V(1) = V(2) = V(3)....
• Resistance is weird. Here goes... R(t) = [R(1)^-1 + R(2)^-1 + R(3)^-1...]^-1

Terminal Voltage & EMF

• electromotive force - maximum voltage that can be created by a cell
• never obtained in practice because of the internal resistance, r, of the cell

• the voltage that is actually supplied to the external circuit...
• V = E - Ir
• where V is the terminal voltage, E is the EMF, I is the current in the circuit, and r is the internal resistance of the cell

Meters

Galvanometer

• a very sensitive meter - only 25-50 microamps are required for full scale deflection
• deflection of the needle is directly proportional to the current (duh)
• Current Sensitivity is the current required to cause full scale deflection

Ammeter

• used to measure large currents
• a galvanometer is connected in parallel with a shunt resistor
• shunt resistors are very low in value
• Ammeters are always connected in series

Voltmeters

• a galvanometer connected in series with a resistor called a multiplier, which happens to have a relatively high value (unlike the shunt resistor)
• voltmeters are always connected in parallel

Voltmeter Sensitivity

• this is a value printed on the meter - measured in ohms/volt
• it states how many ohms of resistance are in the meter when it is registering full deflection
  eg 30,000 ohm/volt means that on the 10V scale, the meter has a resistance of 300,000 ohms
  
• sensitivity can also be used to measure current sensitivity
  eg 1V / 30,000 ohm = 0.000 033A
  
• the higher the ohm/volt, the less current is disturbed

Power

• heat is generated as a result of collisions between electrons and atoms in a wire - this accounts for power lost in a circuit
• power is the rate of using or supplying energy
• measured in watts....1W = 1J/s
• in electrical terms, P = VI (according to Joule's Law)
• one can re-arrange this by using Ohm's Law..
• P = (I^2)R or P = (V^2)/R
• energy is the product of power and time... E = Pt
• 1kWh = 1000J/s * 3600s = 3.6 * 10^6J