Circular Motion
- To cause an object to move with uniform circular motion a centripetal force is required.
- In uniform circular motion, the object has a constant speed (here the speed is scalar and the magnitude is constant, velocity as the vector is constantly changing along with its direction).
- The object is always accelerating as the direction of motion is constantly changing.
- The objects acceleration always acts towards the centre and this is called centripetal acceleration.
- To cause this acceleration, there must be a resulting force acting towards the centre (centripetal force)
F = I / T
r = radius / m
v = velocity/ms-1
w = angular velocity/ rad s-1
f = frequency/ Hz (s-1)
a = acceleration / (ms-2)
F = centripetal force /N
m = mass / kg
T = time / s
w = v / r = 2πf
a=v2/r = w2r
F= mv2/r = mw2r
Motion in vertical circles-The centripetal force is the resultant force and remains constant.
Centripetal force is the resultant force of T (tension in the string) and mg.
Fc = T+ mg
Now the weight ‘fights against’ the tension and must be overcome, so T increases.
Fc = T – mg
Simple Harmonic Motion
It is a type of periodic motion or oscillation where the acceleration is directly proportional to the displacement, but acts in the opposite direction.
Phase difference ‘ᶲ’describes the relationship between two systems – normally expressed in radians.
ᶲ = 2π∆t/T
Mass on a spring x
Energy in SHM
Assuming that there is no friction or air resistance , so total energy remains constant.
Resonance
Natural Frequency= the frequency a system “likes’ to oscillate at.
System can be driven = Energy supplied to the system.
Resonance occurs when a system is driven at its natural frequency
At resonance, energy transfer will be greatest and the amplitude of oscillation will be maximum.
Damping
- Reduces the amplitude of oscillation
- reduces the “sharpness” of resonance peak and “flattens” it.
Thermal energy transfer
INTERNAL ENERGY- is the total of the random kinetic energy due to the motion of the molecule and the potential energy due to the molecules.
Potential Energy – is the energy as the result of the attraction of the molecules.
First law od thermodynamics:
The change in the internal energy is equal to the total energy transferred due to work done and heating.
Specific heat capicity (c) – is the energy required to raise one unit of mass of the object by one unit of temperature.
Latent Heat – total energy absorbed or released when a substance changes its physical state completely at a constant temperature.
Specific latent heat of fusion- is the quantity of heat required to change 1Kg of solid in to liquid at constant temperature.
Specific latent heat of vaporization – is the quantity of heat energy required to change 1Kg of liquid to vapors at constant temperature.
Ideal gases
Absolute zero: the lowest possible temperature, the temperature at which an object has minimum internal energy.
Ok = -273°C
Gas laws
Boyle law : states that
pressure is inversely proportional to volume at constant temperature.
Charles’ law: states that
volume is proportional to temperature at constant pressure.
Pressure law: states that
pressure is directly proportional to temperature at constant volume.
putting these laws together
A ideal gas is one that follows this relationship.
The ideal gas equation
Molecular mass = number of mass * molar mass
Avagodros constant Na: number of atoms in 1Kg of Carbon-12 is used to define the mole, its value is 6.022×1023mol-1.
Kinetic theory of gases
effect of temperature on the distribution of speed
Assumption of the kinetic theory of gases
- The molecules are point molecules. the volume of each molecule can be compared to the volume of gas.
- The molecules have no attraction or repulsion for each other, if they did, the effect would reduce the impact on the walls of container.
- The molecules move around in continuous random motion
- the collisions between the molecules are completely elastic.
Each collision with container surface is much shorter in duration than between the imparts.
Mean kinetic energy of molecules
Total kinetic energy
