znotes Flashcards
Radian
One radian is the angle subtended from the center of the circle by an arc length equal to the radius of the circle
Angular displacement
The angle through which an object has moved through a circle
Angular velocity
The rate of change of the angular position of an object as it moves along a curved path
ω= θ / t
ω= 2π / T = 2πf
Linear velocity
v = ωr
Centripetal force
Resultant force acting on an object perpendicular to its linear velocity towards the center of the circle. Causes circular motion.
F= mv^2 / r = mrω^2
Centripetal acceleration
Derived by equating Newton’s 2nd law and centripetal force
ma = mrω^2 a = rω^2 = v^2/r
Gravitational field strength
The force experienced per unit mass at a point in the gravitational field
g= GM/r^2
Newton’s law of gravitation
The gravitational force present between two masses is directly proportional to the product of the two masses and inversely proportional to the square of their separation.
F = GMm/r^2
Gravitational potential
The work done per unit mass in bringing a point mass from infinity to a point in the gravitational field
ϕ = −GM/r
Gravitational potential is negative because its maximum value is 0 at infinite distance away from the mass
gpe = mgh can be used on Earth’s surface
Gravitational potential energy
The work done in bringing a point mass from infinity to a point in the gravitational field
U = mϕ = −GMm/r
Centripetal acceleration
For an orbiting satellite the cnetripetal force is provided by the gravitational field
GMm/r^2 = mv^2/r v^2 = GM / r
Geostationary orbit
It is always above a fixed point on the equator of the Earth
Fixed period of 24hrs
Moves from West to East - same direction as Earth
Escape velocity of a satellite
Initial KE + Initial GPE = 0
1/2mv^2 = GMm/r
v = (2GM/r)^ 1/2
Avogadro constant
Number of molecules present in 12g of carbon-12
Ideal gas
A gas which obeys the ideal gas equation for all temperatures, pressures and volumes.
pV = nRT
where R = 8.31
Kinetic theory of gases
Negligible intermolecular forces of attraction
Volume of particles negligible to the volume of space between them
Collisions between particles are perfectly elastic
Time for collisions negligible between the time between collisions
Average kinetic energy is proportional to the temperature
Mean square velocity < c >^2
Mean value of the square of the velocities of the molecules
Molecular movement and pressure
pV = 1/3 Nm< c >^2 pV = 1/3 nMr< c >^2
Kinetic energy of a molecule
K.E. = 1/2 m< c >^2
derived by equating two formulae in pV
3/2 kT = Ek
Therefore kinetic energy of particles is directly proportional to the temperature.
Thermal equilibrium
When two or more objects in contact have the same temperature so there is no net flow of energy between them
Absolute zero
Temperature at which a system has minimum internal energy
