Circular Motion
Formula
1. Fcp = mv2 / r = mw2r
2. V = wr
3. Acp = v2 / r = w2r
Extra Notes
- Fcp ⟂ v so force doesn’t change magnitude of v. It only changes direction.
Gravitational Fields
Terms
1. Gravitational Field
- Region where an object experiences gravitational force
2. Gravitational Field Strength
- Net gravitational force per unit mass
3. Gravitational Force
- Attractive force between 2 objects
4. Newton’s Gravitational Law
- The magnitude of attractive force between 2 objects is directly proportional to the
product of the masses & inversely proportional to the squared distance between
them
5. Orbiting Velocity
𝐺𝑀
- v= 𝑟
6. Keppler’s Law
- T2 = (4π2/GM)r3
- The square period of a planet and the Sun is directly proportional to the cube
distance
7. Gravitational Potential
- Work done per unit mass in bringing a point object from infinity to a point
8. Gravitational Potential Energy
- Work done in bringing a point object from infinity to a point
9. Escape Velocity
- Minimum velocity required for object to escape from gravitational field of planet
Essay Questions
1. By reference to the definition of gravitational potential, explain why gravitational
potential is a negative quantity.
- Gravitational potential at infinity is 0
- Gravitational force is attractive so work is done as object moves from infinity (so
potential is negative)
2. State the features of a geostationary orbit.
, - Remain above the same point on the Earth and has a period of 24 hours
- Equatorial orbit
- From west to east
3. Explain how a satellite may be in a circular orbit around a planet.
- Gravitational force provides centripetal force (on satellite about the planet)
4. Explain why, for changes in vertical position of a point mass near the Earth’s
surface, the gravitational field strength may be considered to be constant.
- Changes in height much less than radius of Earth
- So radial field lines are almost parallel
5. State what is meant by a line of force in a gravitational field.
- Direction of force on a small test mass
6. By reference to the pattern of the lines of gravitational force near to the surface of
the Earth, explain why the acceleration of free fall near to the Earth’s surface is
approximately constant.
- The lines are radial
- Near the surface, the lines are approximately parallel
- Parallel lines mean constant field strength
Thermodynamics
Terms
1. Ideal Gas
- Gas that obeys PV = nRT / PV = NKT
- P = Pressure, V = Volume, T = Temperature
- nR & NK are constant
2. Gas Laws
a. Boyle’s Law ( Constant temperature )
- PV = PV
b. Charles’ Law ( Constant pressure )
𝑉 𝑉
- 𝑇
= 𝑇
c. Gay-Lussac’s Law ( Constant volume )
𝑃 𝑃
- 𝑇
= 𝑇
3. Avogadro constant NA
- Number of atoms in 0.012 kg of Carbon-12
4. Mole
- Amount of substance which contains as many elementary entities as there are
atoms in 0.012 kg of Carbon-12
5. Kinetic Theory of Gases
a. All molecules behave as identical, hard, elastic spheres
b. Volume of molecules are negligible compared to volume of containers
c. Molecules are moving randomly to all directions
d. No interaction between molecules ( no repulsive & attractive forces )
e. Collisions between molecules & the wall of the container are perfectly elastic
, 6. Temperature
- Degree of average kinetic energy of molecule in substance
7. Specific Heat Capacity
- Energy required to increase temperature of 1 kg substance by 1°C = 1K
8. Specific Latent Heat Of Fusion
- Heat required to change the state of 1 kg substance from solid to liquid without
changing its temperature
9. Internal Energy
- Sum of total KE & PE in random distribution
10. Thermodynamics Process
Process W Δ𝑢 Q
Isobaric (Constant P) PΔV ≄0 ≄0
Isochoric / Isovolume 0 ≄0 ≄0
(Constant V)
Isothermal (Constant T) ≄0 0 ≄0
W = nRTln(V2 / V1)
Adiabatic ≄0 ≄0 0
Formulae
1
1. PV = 3
Nm <c2>
3
2. Average KE of Molecules → < EK > = 2
kT
3. PT = Q + h
3
4. 𝑢 = KEtotal = N( 2 kT ) → If PE is 0
5. Δ𝑢 = Q + W
Essay Questions
1. Suggest suitable types of thermometer to measure:
a. Temperature of the flame of a Bunsen burner → Thermocouple
b. Change in temperature of a small crystal when it is exposed to a pulse of
ultrasound energy → Thermistor
2. a. State
i) what may be deduced from the difference in the temperatures of 2 objects
- Direction / rate of transfer of thermal energy
ii) basic principle by which temperature is measured
- Uses a property ( of a substance ) that changes with temperature
b. By reference to your answer in (a)(ii), explain why 2 thermometers may not give
the same temperature reading for an object
Formula
1. Fcp = mv2 / r = mw2r
2. V = wr
3. Acp = v2 / r = w2r
Extra Notes
- Fcp ⟂ v so force doesn’t change magnitude of v. It only changes direction.
Gravitational Fields
Terms
1. Gravitational Field
- Region where an object experiences gravitational force
2. Gravitational Field Strength
- Net gravitational force per unit mass
3. Gravitational Force
- Attractive force between 2 objects
4. Newton’s Gravitational Law
- The magnitude of attractive force between 2 objects is directly proportional to the
product of the masses & inversely proportional to the squared distance between
them
5. Orbiting Velocity
𝐺𝑀
- v= 𝑟
6. Keppler’s Law
- T2 = (4π2/GM)r3
- The square period of a planet and the Sun is directly proportional to the cube
distance
7. Gravitational Potential
- Work done per unit mass in bringing a point object from infinity to a point
8. Gravitational Potential Energy
- Work done in bringing a point object from infinity to a point
9. Escape Velocity
- Minimum velocity required for object to escape from gravitational field of planet
Essay Questions
1. By reference to the definition of gravitational potential, explain why gravitational
potential is a negative quantity.
- Gravitational potential at infinity is 0
- Gravitational force is attractive so work is done as object moves from infinity (so
potential is negative)
2. State the features of a geostationary orbit.
, - Remain above the same point on the Earth and has a period of 24 hours
- Equatorial orbit
- From west to east
3. Explain how a satellite may be in a circular orbit around a planet.
- Gravitational force provides centripetal force (on satellite about the planet)
4. Explain why, for changes in vertical position of a point mass near the Earth’s
surface, the gravitational field strength may be considered to be constant.
- Changes in height much less than radius of Earth
- So radial field lines are almost parallel
5. State what is meant by a line of force in a gravitational field.
- Direction of force on a small test mass
6. By reference to the pattern of the lines of gravitational force near to the surface of
the Earth, explain why the acceleration of free fall near to the Earth’s surface is
approximately constant.
- The lines are radial
- Near the surface, the lines are approximately parallel
- Parallel lines mean constant field strength
Thermodynamics
Terms
1. Ideal Gas
- Gas that obeys PV = nRT / PV = NKT
- P = Pressure, V = Volume, T = Temperature
- nR & NK are constant
2. Gas Laws
a. Boyle’s Law ( Constant temperature )
- PV = PV
b. Charles’ Law ( Constant pressure )
𝑉 𝑉
- 𝑇
= 𝑇
c. Gay-Lussac’s Law ( Constant volume )
𝑃 𝑃
- 𝑇
= 𝑇
3. Avogadro constant NA
- Number of atoms in 0.012 kg of Carbon-12
4. Mole
- Amount of substance which contains as many elementary entities as there are
atoms in 0.012 kg of Carbon-12
5. Kinetic Theory of Gases
a. All molecules behave as identical, hard, elastic spheres
b. Volume of molecules are negligible compared to volume of containers
c. Molecules are moving randomly to all directions
d. No interaction between molecules ( no repulsive & attractive forces )
e. Collisions between molecules & the wall of the container are perfectly elastic
, 6. Temperature
- Degree of average kinetic energy of molecule in substance
7. Specific Heat Capacity
- Energy required to increase temperature of 1 kg substance by 1°C = 1K
8. Specific Latent Heat Of Fusion
- Heat required to change the state of 1 kg substance from solid to liquid without
changing its temperature
9. Internal Energy
- Sum of total KE & PE in random distribution
10. Thermodynamics Process
Process W Δ𝑢 Q
Isobaric (Constant P) PΔV ≄0 ≄0
Isochoric / Isovolume 0 ≄0 ≄0
(Constant V)
Isothermal (Constant T) ≄0 0 ≄0
W = nRTln(V2 / V1)
Adiabatic ≄0 ≄0 0
Formulae
1
1. PV = 3
Nm <c2>
3
2. Average KE of Molecules → < EK > = 2
kT
3. PT = Q + h
3
4. 𝑢 = KEtotal = N( 2 kT ) → If PE is 0
5. Δ𝑢 = Q + W
Essay Questions
1. Suggest suitable types of thermometer to measure:
a. Temperature of the flame of a Bunsen burner → Thermocouple
b. Change in temperature of a small crystal when it is exposed to a pulse of
ultrasound energy → Thermistor
2. a. State
i) what may be deduced from the difference in the temperatures of 2 objects
- Direction / rate of transfer of thermal energy
ii) basic principle by which temperature is measured
- Uses a property ( of a substance ) that changes with temperature
b. By reference to your answer in (a)(ii), explain why 2 thermometers may not give
the same temperature reading for an object
