Newton's 1st Law of Motion
An object will continue in a state of rest or of uniform motion in a straight line unless acted upon by a resultant force
Newton's 2nd Law of Motion
The rate of change in momentum of an object is proportional to the resultant force and in the same direction
Newton's 3rd Law of Motion
If object A exerts a force on object B, then B exerts an equal and opposite force on A
Momentum
mass x velocity
Inelastic Collision
Momentum conserved, KE decreases, objects stick together
Perfectly Elastic Collision
Momentum conserved, KE conserved, bounce off each other
Newton's Law of Restitution
Relative speed of approach = relative speed of seperation
Hydrogen Atom
1 Proton, 1 Electron
Helium Atom
2 Protons, 2 Neutrons, 2 Electrons
Oxygen Atom
8 Protons, 8 Neutrons, 8 Electrons
Carbon Atom
6 Protons, 6 Neutrons, 6 Electrons
Explosion
Momentum Conserved, KE decreases, stick together
1 radian
The angle subtended by an arc length equal to the radius
Arc Length, s
r?
Defining equation of SHM
a = - (2?f)� x
Frequency of oscillations
Number of oscillations per unit time
Frequency, f
1 / T
Xmax
A
Vmax
A(2?f)
amax
A(2?f)�
SHM: t = 0, x = 0
x = Asin(2?ft)
SHM: t = 0, x = A
x = Acos(2?ft)
Simple harmonic motion
The acceleration of an object is proportional to its displacement from a fixed point and directed towards that fixed point
SHM displacement
Distance moved from fixed point
SHM amplitude
max displacement
SHM angular frequency
2?f
Forced Oscillations
We superimpose a periodic driving force and make the system oscillate at the driving frequency
Natural Frequency
Frequency at which resonance occurs
Period of an object with SHM
is independent of its amplitude
SHM Energy Change
KE and PE swap, total energy is constant
Damping
Any mechanism that converts energy of the oscillating system irreversibly into other forms of energy
Critical Damping
No oscillation occurs and body moves back to equilibrium position in minimum time
Resonance
The build up of a large amplitude oscillation when the frequencies of vibrating objects match (i.e. driving frequency = natural frequency)
Free Oscillations
System is displaced from equilibrium and allowed to oscillate at its natural frequency
Practical uses of resonance
Microwave Ovens, Radios, MRI scans, Musical Instruments
F=ma
Special case of Newton's second law when mass remains constant
Impulse
Change in Momentum
Area under f/t graph
equal to impulse
Grav field strength (at a point)
Force per unit mass on a small test mass placed at a point.
Principle of conservation of momentum
in any direction, in the absence of external forces, the total momentum of a system remains constant
Newtons law of gravitation
The gravitational force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them
By newtons law of gravitation
F = -(GMm) / r�
Geostationary orbit of a satellite
An orbit centered on the centre of the earth travelling from West to East, over the equator with a period of 24 hours
Centripetal Force, F
mv�/r
Centripetal acceleration, a
r?� = v� / r = v?
Angular velocity, ?
??/?t
Circular velocity, v
r? =2?r / T
For a satellite
v� = GM / r
Time period, T
2?r / v
T�
(4?�/GM)r�
Gravitational field strength, g
-GM / r�
Phase
Whether a substance is solid, liquid or gas
Density
Mass per unit volume
Thermal energy
transferred from a region of higher temperature to a region of lower temperature
One mole of any substance
contains 6.02 x 10�� atoms
The ideal gas equations
NkT and pV = nRT, where N is the number of atoms, n is the number of moles and R is the molar gas constant.
Mean KE of a single molecule (Internal Energy), E
3/2 kT
Mean transitional kinetic energy of an atom of an ideal gas
is directly proportional to the temperature in K
Specific heat capacity
Thermal Energy required to raise the temperature of a unit mass by a unit temperature rise
Thermodynamic scale
absolute scale of temperature
Absolute Zero
0k, -273.15 �C, Min Internal Energy
T(K)
#NAME?
Assumptions of kinetic theory of gas
large number of molecules in random rapid motion, elastic collisions, no intermolecular forces, total volume of molecules is negligible
Boyles Law
Volume of fixed mass of gas is inversely proportional to the pressure exerted on it provided T is constant
Triple point
Temp at which substance can be solid, liquid, gas
pV / T
constant
SHC, c
E / m??
Electrical experiment to determine SHC
Measure mass, heat with electrical heater, measure temp, plot temp / time, measure gradient, c = VI / (m x gradient)
Specific Latent heat of Fusion
The quantity of energy per unit mass required to change it at constant temp from solid into liquid.
Specific Latent Heat of Vaporisation
The quantity of energy per unit mass required to change it at constant temp from liquid into gas.
Internal energy
Sum of random distributions of kinetic and potential energies of the molecules of a substance
Ideal gas
has Internal energy only in the form of random kinetic energy
Pressure
Perpendicular Force per unit area
A rise in temperature
means higher KE of molecules, so higher internal energy
A change of state
leads to changes in internal energy due to changes in the random PE of molecules.
Brownian motion
random motion of particles in a fluid