Rotational Motion Rotational equivalent of force = Torque = Fr sin ! ; r = distance between axis and force Rotational equivalent of mass = Moment of inertia = I. TorqueNET = I x angular acceleration - I is always a multiple of mr 2 - Inertia is greater the further the mass is from the axis of rotation. KE of a rotating body =
KE
=
1 2
I ! !
2
Total KE of a body bod y with translational + rotational rotationa l movement =
KE =
Rotational equivalent of momentum = angular momentum = L Angular acceleration =
=
1 2
2
! + I !
1 2
2
mvcm
I !
!! !t
Angular velocity has right hand rule - Closed fist, fingers point in direction of rotation, thumb towards direction of angular velocity vector Dynamics Friction = f = µN; N = normal force Energy/Work/Power Us =
1
kx
2
2
; k = spring constant, x = displacement
Circular motion - minimum speed occurs when tension is zero at the top of the loop Gravity G = constant (6.67 x 10 -11 ) mM Force acting on acting on two planets (equal and opposite) separated by distance r distance r:: F g G 2 r M Gravity (whe hen n an an ob object mov moves es in a manne nerr th that chang nge es g) g) = g G 2 ; r = di distan anc ce fr from ce center ter r of planet, M = mass of planet =
=
Velocity of orbiting satellites = KE =
1 2
vorbit
GM =
r
F c R 2
3
Elliptical orbit - T r , where T = period of orbit, r = radius in orbit about sun - i.e. T2 / r3 = constant !
Keplers Laws: 1) Planets orbit the sun along an elliptical path where the sun is one of two foci. foci. 2) The orbiting body moves faster when it is nearer the central body 2 3 3) T r !
Electric fields Like charges repel like charges charges. Field lines point away positive charges, towards negative charges. Direction is same as direction of force acting on positive charge. charge. Charge always resides on the surface of a conductor If a charge is placed into a uniform electric field, it will experience a force FE (the same way a mass in a gravitational field experiences mg). Field exerted by plane charge = kq
Fe = qE (positive charge = force in direction of field E, negative charge = force is opposite field) Point charges - Charges where electric field is calculated as though it originates from a single point (i.e. electrons, protons, ions). - Field radiates outwards. - When two charges are brought near each other, they interact Magnitude of a electric field E = k
q
; k = electrostatic constant 9 x r2 109 Nm2C-2, r is distance from center of charge. Superposition - Net force = vector sum of forces acting on a particle
q q Coulombs law (resulting force acting on both charges) = FE = k 1 2 2 ; r where r = distance between to charges Work done to move charge = Fqd = qED. -When the charge moves a distance r parallel to the electric field lines, the work done is qEr. - When the charge moves a distance r perpendicular to the electric field lines, no work is done. - When the charge moves a distance r at an angle to the electric field lines, the work done is qEr cos#. Conservation of charge - Total charge is always constant. When two spheres touch, their excess charges are neutralised (if same size, each sphere gets total charge/2) Potential energy = U
! kq q 1
=
2
r
Electric Potential Magnitude of electric potential at a location in a uniform electric field =; d is distance from location where is potential is zero. Field point high to low. V = Ed Potential of point charges - oriented pointing away from positive charges, has a maximum value at surface of charge, becomes weaker with inverse square of distance rom centre. q V k ; when several point charges surround a pont, the total potential is the sum of the r =
individual potentials i.e. Potential energy = U E Moving charges -
!V
=
=
Work of Electricity: W
V T = V 1 + V 2 . + ...
qV =qEd
V f " V i , Vf = final voltage, Vi = initial voltage
=
! K
Conservation of Energy:
1 2
=
! U E
2
=
" q!V
mvmax = q!V
Charged plates - Can store excess charge and energy. Capacitance, C, (measured in farads (F)) = ability to store charge. Q C= for any capacitor !V C
=
! 0 A
d
for a parallel plate capacitor. d = distance between two plates, e0 = constant (permittivity
of free space = 8.85 x 10-12 C2M2N-1), A = area of plates Charge stored in a capacitor = Q = CV. Energy stored in a capacitor = U C
=
1 2
QV
=
1 2
2
CV (energy is required to move charge from
negative to positive)
1 Capacitance in a circuit =
C t C t
=
=
1 C 1
+
1 C 2
(series)
C 1 + C 2 (parallel)
Electricity Joules Law - Heat (Q) dissipated in a circuit = I2Rt Brightness of a Lightbulb = PT= I2R (Brightness = Power) Parallel Resistors receive the same voltage Magnetic Fields Fields go from North to south pole. • = out of page, x= into page (z axis) Direction of field in current carry wire - Right hand rule (point right thumb in direction of current) Magnitude of magnetic field (T)=
B
=
µ 0 I 2! r
, u0 = constant 4# x 10-7; current = I; distance from
center of wire to point where field is measured = r - Strength of field is proportional to strength of current - Weaker the further it is from the wire Magnetic force on moving charge (like electrons) = F B qVB sin ! ; magnetic field = B, theta is angle between velocity and field vector. (When perpendicular, sin theta = 1) =
Charges move at a constant speed in uniform circular motion,
mv r
2 =
qvB .
Charge moving in magnetic fieldRight hand rule - Flat palm, thumb = v, fingers = B, Direction palm pushes = FB Left hand = negative charges Force acting on current-carrying wires = between current and field
F B
=
ILB sin ! ;
L = length of wire inside field, $ = angle
Electromagnetic induction - Generating electricity. Moving magnet induces current to flow through wire. Occurs when amount of field magnetic flux changes. Flux = !
=
BA ,
A = area of space that field passes through.
Two parallel wires with the current in the same direction will attract each other.
Faraday deduced that a changing flux generates an emf. !
=
!" t
*-1= BLv = IR
- (Strength can be increased by moving faster, longer bar, stronger field) SHM Restoring force Fs on a spring = kx - In equilibrium, mg=kx For a spring mass system, the period = For a pendulum, period = T P
=
2 !
L g
T S
=
2 !
m k
(only depends on mass and spring constant)
L = length of string (mass has no effect, only length)
Waves Beats - Superposition of waves that don’t have the same frequency doesn't give a sinusoidal pattern. Destructive portions cause a decrease in amplitude at a regular rate, called beats
f beat
=
f 1 ! f 2
Intensity is inversely proportional to distance Geometric Optics Less Dense medium- Dense - $1 > $2 Dense medium- Less Dense - $2 > $1 Dense = high value for n, small angle of refraction = high n Pinhole camera - Reflection Magnification of image =
M
=
hi ho
=
d i
!
d o
; ho = object height, hi = object height do = object
distance from pinhole, di = image distance from pinhole (small, inverted images formed with negative height) Convex lens - formed by the intersection of two spheres. f, focal length = radius R/2 Converging lenses (i.e. convex lens) bring light together. Where light intersects = where the image is focused. - Light parallel to the optical axis (radius of circle) converges on far focal point. - Light that passes through the center of the lens moves in a straight line. 1
f
=
1
d O
+
1
d i
, focal length of lens = f, object distance to lens = do, image distance from lens = di
Magnification formula also applies. If object is - outside the focus, f, the image is inverted and real.
- inside f, the image is upright and virtual. - at f, no image is formed. Diverging Lenses spread light out, always forms a small upright virtual image. Spherical Mirrors - Section of a sphere with a reflective surface (inside of sphere for concave, outside for convex) Converging mirrors are concave, diverging mirrors are convex. Mirrors form real images on the near side, virtual images on the far side. (Real on far side, virtual on near side for lenses)
Physical Optics Diffraction - Shadow region is area where there are no wave fronts. Double Slit Experiment Distance between central maximum and maximum bend investigated = xm, spacing between slits = d, m = number of maximum investigated xm
m! L =
d
; d
=
m ! sin "
Color - Object of a certain color is reflecting that color, absorbing all other colours. Dispersion - Wavelengths of light from the sun can be separated via dispersion. Seen using prism. Each color has a slightly different wavelength + angle of refraction, so it bends at a slightly different angle. Short wavelengths have highest index of refraction, bend the most. Thermal An object being heated/cooled expands/contract ! L
=
! L0 !T
& = coefficient of linear expansion L0 = original length
Rectangular area - use twice, once with widht, once with height. Rate of heat transfer -
Q !t
=
kA!T L
Heat Engine - Converts thermal energy to other forms. Operate between a hot temperature TH and a low temperature TC, heat QH is added to the engine, heat Qc is removed from the engine at low temp. W = QH- QC QH = input, W = useful work, Theoretical maximum is when W = QH- QC (TEMP IN KELVIN)
Atomic/Quantum Phenomena hc hf Energy of a photon = E =
!
=
Absorption - Photon energy + Initial electron Energy = New Energy Level, drawn as upward arrow. Emission = Light given off by an atom when electrons drop to lover energy levels = difference in energy levels. Drawn with downward arrows. - “All possible energies” = all possible drops from a certain energy level Balmer series - Transitions to n=2, visible light Lyman series - Transitions to n=1, UV light If energy of incoming photons is greater than energy between ground state and edge of atom, electrons are ejected (ionisation). Ionisation energy = $ = |Eground state| When electrons leave, they will be travelling with excess energy (max KE) = EPhoton - $ Light causing electrical discharge is the photoelectric effect. Light with a minimum threshold frequency can induce the emission of electrons from metal. The emitted electrons can ebe collecte, creating a potential difference (photo cell) - Adjusting the frequency of light results in the release of electrons above a threshold frequency. - Above this frequency, energy of emitted electrons is proportional to frequency. Atomic/Quantum Phenomena
Nucleons = (Protons + Neutrons) Alpha - Nucleus of helium atom without electrons Beta particle - Electron produced when neutron undergoes transmutation to become a proton i.e. 1 n -> 1 p + 0 e 0 1 -1 Neutrino - Product of radioactive decay/nuclear reactions Mass defect - Small amount of mass that is converted to energy during nuclear reaction. E
=
! mc
2
Mass - energy equivalence - Under certain conditions, matter may be converted to energy or energy may be converted to matter. Alpha decay - Ejection of an alpha particle (subtract 4 from mass no, 2 from atomic number) Beta decay - Ejection of an beta particle (add 1 to atomic number as nucleon -> proton + electron, electron leaves) Fission - Large nucleus into smaller nuclei Fusion - Large nucleus from smaller nuclei Relativity An object moving near light speed results in Time dilation - A clock on the object will appear to move slowly, passengers on the object will appear to be in slow motion
Length contraction (only affects direction of motion) - Length in direction of the motion will appear to decrease if viewed by a stationary observer Mass increase - The mass of a moving object will appear to increase if seen by a stationary observer. Special relativity - Laws of physics are the same in all intertial reference frames - Speed of light is a constant regardless of the motion of the observer or light source Historical Figures/Contemporary Physics Newtonian Mechanics Galileo - Bodies dropped fall with acceleration g, x=0.5gt2 - Principle of Inertia - Natural state of motion is uniform constant velocity Newton - 1st Law - Every body continues in a state of rest or uniform velocity unless acted upon by a unbalanced force. - 2nd Law - F=ma - 3rd Law -If body A exerts a force on body B, then body B exerts an equal and opposite force on body A. - Law of gravity - Two masses m1 and m2 at a distance of r attract each other. James Watt - Power Kepler - Laws of planetary motion - Planetary motion is elliptical - Line drawn from central body to orbiting body will sweep equal areas of space in equal time intervals - T2 is proportional to r3 Electricity and Magnetism Coulomb - Two charges will attract/repel eacother Ohm - Ohms law V=IR Faraday - Electromagnetic fields - Electromagnetic induction Lenz - Lenz’s Law dictates direction of induced current in a loop of conducting material
Maxwell - Demonstrates light is an EM wave Waves/Optics
Young - Double slit experiment Doppler - Doppler Shift Thermal Kelvin Absolute Zero Joule -Heat and work equivalence - both are ways to add energy to a system. Modern Physics Michelson/Morley - Designed a device known as a interferometer to detect the motion of earth through ether, failed to prove its existence Thomson - Discovered the electron Planck - Founded Quantum theory Einstein - Photoelectric effect E=hf - When EM radiation shines on a metal, the surface of the metal absorbs energy, some electrons fly off (photoelectrons).
- KE = hf - (work function) (i.e. y intercept = -w) - Threshold function - Frequency to
- Special relativity - E=mc2 - Mass- energy equivalence
- Binding energy = (mass of nucleons - mass of nucleus)c2 Rutherford - Gold foil Niels Bohr - Planetary model of the atom, energy levels Contemporary Physics Astrophysics - Physics of celestial objects, resolve the origin of the universe Chaos Theory - Explain the behaviour of complex and chaotic systems. Dark Matter - Total mass of the universe does not match gravitational effects; matter that cannot be seen accounts for missing mass Microprocessor - Single circuit consisting of miniaturised components
Semiconductor - Material that can act as either conductor or insulator i.e. silicon Superconductivity -Material with 0 resistance below a critical temperature String theory - Elementary particles are actually in ear oscillations Transistor - Amplify electrical signal, act as a switch Optics 2 All rays of light that run parallel to the principal axis are reflected/refracted through the focal point F (and a ray of light that passes through the focal point will be reflected parallel to the axis). Focal length, f, = distance between focal point and vertex. Real image - formed by actual rays of light (if you held up a screen, the image would be projected). In front of mirror. Virtual image - no light actually forms the image (behind mirror) Concave mirrors Behind focal point - real inverted image created. In front of focal point - virtual upright image. Convex Mirror - Focal point is behind mirror, light parallel to principal axis is
reflected away from focal point. Light going towards the focal point Virtual upright image (behind mirror between mirror and focal point)
Focal length:
1
+
1
=
1
d d ' f d’ = image, d = object - f>0 - converging, f<0 - diverging - If d’ is negative, image is virtual, d’ is positive, image is real - Positive = outgoing light side - if d is positive
Magnification:
m
h' =
h
! d
'
=
d
- m = magnification - If |m|>1, image is larger, vice versa - h= height of object, h’ = height of image - if h’ is positive, image is upright, vice versa Convex Lens - Behaves like mirror but uses refraction not reflection. - Ray of light that passes through vertex does not get refracted - Focal point is behind lens - d (distance of object from lens)>f - real, inverted, opposite side of lens (opposite side as object) - d
Double Slit ! d
x =
L
d = distance between slits, L = distance between screens, x = distance between
maximums
