CIE GCE A LEVEL PHYSICS [9702] GLOSSARY & FORMULAES
TOPIC 12 AND 13 – CIRCULAR MOTION AND GRAVITATIONAL FIELDS
RADIAN [RAD] the angle subtended at the center of a circle such that the arc length equals to the radius.
ANGULAR VELOCITY 𝝎 rate of change of angular displacement
[𝒓𝒂𝒅 𝒔!𝟏 ] 𝚫𝜽 𝟐𝝅
𝝎= =
𝚫𝒕 𝑻
(where T is the period of circular motion)
RELATING VELOCITY & 𝝎 𝒗 = 𝒓𝝎
UNIFORM CIRCULAR MOTION Deduction from the Equation:
• changing direction of velocity
• constant magnitude of velocity
• acceleration ⊥ velocity
• an object in circular motion, must experience centripetal force
CENTRIPETAL FORCE [N] Centripetal force is perpendicular to the velocity in a circular motion.
𝒎𝒗𝟐
𝑭𝑪 = = 𝒎𝒓𝝎𝟐
𝒓
CENTRIPETAL ACCELERATION 𝒎𝒗𝟐
𝑭𝑪 𝒗𝟐
𝒂= = 𝒓 = = 𝒓𝝎𝟐
𝒎 𝒎 𝒓
GRAVITATIONAL FIELD a region of space where a mass experience (gravitational) force
MEANING OF LINE OF FORCES The direction of force/acceleration on a (small test) mass
NEWTON’S LAW OF F is proportional to the product of masses and inversely proportional to the separation squared, where force is between the masses.
GRAVITATION [N] 𝑮𝒎𝟏 𝒎𝟐
𝑭=
𝒓𝟐
GRAVITATIONAL FIELD Gravitational force on a point mass per unit mass.
STRENGTH 𝑮𝒎
𝒈=
𝒓𝟐
,PATTERNS OF G-FIELD LINES Patterns of G-field/force Lines
(AND HOW IT LEADS TO • radial field lines
CONSTANT ACCELERATION OF • field lines approx. parallel on surface
FREE FALL)
Thus:
• parallel lines = constant gravitational field strength
• constant g = constant acceleration of free fall (F=ma=mg)
GRAVITATIONAL POTENTIAL Work done by an external force against the gravitational force in moving a mass from infinity to the present location.
ENERGY [J] 𝑮𝒎𝟏 𝒎𝟐
𝒖=−
𝒓
GRAVITATIONAL POTENTIAL Work done per unit mass by an external force against the gravitational force in moving a mass from infinity to the present location.
𝑮𝒎 𝑮𝑷𝑬
𝑽=− =
𝒓 𝒎
WHY GRAVIATIONAL • the radius of a planet MUCH GREATER than changes in height
POTENTIAL IS APPORX. • since potential is inversely proportional to radius, and radius is constant
CONSTNAT WITH SMALL • potential is constant approximately
CHANGES IN HEIGHT NEAR A
PLANET’S SURFACE
ESCAPE VELOCITY [M/S] Minimum velocity required for an object to escape the gravitational field of a planet.
𝟐𝑮𝒎
𝒗𝒆𝒔𝒄𝒂𝒑𝒆 = 9
𝒓
(where m is the mass of the planet)
,RELATING GRAVITATIONAL 𝒅𝑽
𝒈=−
POTENTIAL AND 𝒅𝒓
GRAVITATIONAL FIELD
STRENGTH (negative gradient of a potential-radius graph)
KEPLER’S LAW 𝒎𝒗𝟐 𝑮𝒎𝟏 𝒎𝟐
𝒃𝒚, =
𝒓 𝒓𝟐
𝒓𝟑
𝑻 = 𝟐𝝅9
𝑮𝒎
(𝑇 + ∝ 𝑟 , )
DENSITY AND FIELD -
Volume of Sphere = 𝜋𝑟 ,
,
STRENGTH Mass = Volume*Density
𝟒𝑮𝝆𝝅𝒓
𝒈=
𝟑
GEOSTATIONARY ORBIT • Period = 24 Hours
• Above Equator
• Orbits West à East
• One Particular Orbit (fixed radius)
, TOPIC 14, 15, 16 –TEMPERATURE, IDEAL GAS, THERMODYNAMICS
DESCRIPTION OF STRCUTURE • particles/atoms/molecules/ions close together
OF A SOLID WITH MATTER • regular, repeating pattern
MODEL • vibrate at a fix point
THERMAL ENERGY/HEAT Energy transferred due to difference in temperature.
TEMPERATURE A measure of average kinetic energy of molecule in a system, and shows the direction of the net heat flow between two bodies.
SPECIFIC HEAT CAPACITY Thermal energy required per unit mass to change the temperature of a substance by 1K.
[J/KG K] 𝑸 = 𝒎𝒄∆𝑻
SPECIFIC LATENT HEAT [J/KG] Thermal energy required per unit mass for a substance to change its state at constant temperature.
𝑸 = 𝒎𝒍
THERMAL EQUILIBRIUM Two objects are in thermal equilibrium if they are at the same temperature.
AVOGADRO’S CONSTANT 𝑁. is the number of atoms in 12g of Carbon-12
𝑵𝑨 = 𝟔. 𝟎𝟐 × 𝟏𝟎𝟐𝟑
MOLES [MOL] The amount of substance containing 𝑁. atoms.
0
(number of moles) 𝑛 = 0 (number of molecules/Avogadro’s constant)
!
IDEAL GAS 12
A gas obeying = constant
3
where P = pressure; V = volume; T = temperature
𝑷𝑽 = 𝑵𝒌𝑻 𝑷𝑽 = 𝒏𝑹𝑻
!+, !4
where Boltzmann’s Constant k = 1.38 × 10 𝐽𝐾 where Molar Gas Constant R = 8.31 𝐽 𝑘 !4 𝑚𝑜𝑙 !4
If Temperature of Gas is constant: If Volume of Gas is constant: If Pressure of Gas is constant:
1 𝑃∝𝑇 𝑉∝𝑇
𝑃∝
𝑉
KINETIC THEORY OF IDEAL • [Molecules in] Random Motion (gravity negligible)
GAS • NO intermolecular force between molecules (PE = 0)
• Collisions are instantaneous (time between collision >> time during collision)
• Molecules have negligible volume compared to volume of container
• Collisions are elastic (no KE loss/total KE conserved)
∵ no intermolecular force between moleucles
∴ PE = 0, Internal Energy = Kinetic Energy à Avg. KE ∝ T à IE ∝ T
TOPIC 12 AND 13 – CIRCULAR MOTION AND GRAVITATIONAL FIELDS
RADIAN [RAD] the angle subtended at the center of a circle such that the arc length equals to the radius.
ANGULAR VELOCITY 𝝎 rate of change of angular displacement
[𝒓𝒂𝒅 𝒔!𝟏 ] 𝚫𝜽 𝟐𝝅
𝝎= =
𝚫𝒕 𝑻
(where T is the period of circular motion)
RELATING VELOCITY & 𝝎 𝒗 = 𝒓𝝎
UNIFORM CIRCULAR MOTION Deduction from the Equation:
• changing direction of velocity
• constant magnitude of velocity
• acceleration ⊥ velocity
• an object in circular motion, must experience centripetal force
CENTRIPETAL FORCE [N] Centripetal force is perpendicular to the velocity in a circular motion.
𝒎𝒗𝟐
𝑭𝑪 = = 𝒎𝒓𝝎𝟐
𝒓
CENTRIPETAL ACCELERATION 𝒎𝒗𝟐
𝑭𝑪 𝒗𝟐
𝒂= = 𝒓 = = 𝒓𝝎𝟐
𝒎 𝒎 𝒓
GRAVITATIONAL FIELD a region of space where a mass experience (gravitational) force
MEANING OF LINE OF FORCES The direction of force/acceleration on a (small test) mass
NEWTON’S LAW OF F is proportional to the product of masses and inversely proportional to the separation squared, where force is between the masses.
GRAVITATION [N] 𝑮𝒎𝟏 𝒎𝟐
𝑭=
𝒓𝟐
GRAVITATIONAL FIELD Gravitational force on a point mass per unit mass.
STRENGTH 𝑮𝒎
𝒈=
𝒓𝟐
,PATTERNS OF G-FIELD LINES Patterns of G-field/force Lines
(AND HOW IT LEADS TO • radial field lines
CONSTANT ACCELERATION OF • field lines approx. parallel on surface
FREE FALL)
Thus:
• parallel lines = constant gravitational field strength
• constant g = constant acceleration of free fall (F=ma=mg)
GRAVITATIONAL POTENTIAL Work done by an external force against the gravitational force in moving a mass from infinity to the present location.
ENERGY [J] 𝑮𝒎𝟏 𝒎𝟐
𝒖=−
𝒓
GRAVITATIONAL POTENTIAL Work done per unit mass by an external force against the gravitational force in moving a mass from infinity to the present location.
𝑮𝒎 𝑮𝑷𝑬
𝑽=− =
𝒓 𝒎
WHY GRAVIATIONAL • the radius of a planet MUCH GREATER than changes in height
POTENTIAL IS APPORX. • since potential is inversely proportional to radius, and radius is constant
CONSTNAT WITH SMALL • potential is constant approximately
CHANGES IN HEIGHT NEAR A
PLANET’S SURFACE
ESCAPE VELOCITY [M/S] Minimum velocity required for an object to escape the gravitational field of a planet.
𝟐𝑮𝒎
𝒗𝒆𝒔𝒄𝒂𝒑𝒆 = 9
𝒓
(where m is the mass of the planet)
,RELATING GRAVITATIONAL 𝒅𝑽
𝒈=−
POTENTIAL AND 𝒅𝒓
GRAVITATIONAL FIELD
STRENGTH (negative gradient of a potential-radius graph)
KEPLER’S LAW 𝒎𝒗𝟐 𝑮𝒎𝟏 𝒎𝟐
𝒃𝒚, =
𝒓 𝒓𝟐
𝒓𝟑
𝑻 = 𝟐𝝅9
𝑮𝒎
(𝑇 + ∝ 𝑟 , )
DENSITY AND FIELD -
Volume of Sphere = 𝜋𝑟 ,
,
STRENGTH Mass = Volume*Density
𝟒𝑮𝝆𝝅𝒓
𝒈=
𝟑
GEOSTATIONARY ORBIT • Period = 24 Hours
• Above Equator
• Orbits West à East
• One Particular Orbit (fixed radius)
, TOPIC 14, 15, 16 –TEMPERATURE, IDEAL GAS, THERMODYNAMICS
DESCRIPTION OF STRCUTURE • particles/atoms/molecules/ions close together
OF A SOLID WITH MATTER • regular, repeating pattern
MODEL • vibrate at a fix point
THERMAL ENERGY/HEAT Energy transferred due to difference in temperature.
TEMPERATURE A measure of average kinetic energy of molecule in a system, and shows the direction of the net heat flow between two bodies.
SPECIFIC HEAT CAPACITY Thermal energy required per unit mass to change the temperature of a substance by 1K.
[J/KG K] 𝑸 = 𝒎𝒄∆𝑻
SPECIFIC LATENT HEAT [J/KG] Thermal energy required per unit mass for a substance to change its state at constant temperature.
𝑸 = 𝒎𝒍
THERMAL EQUILIBRIUM Two objects are in thermal equilibrium if they are at the same temperature.
AVOGADRO’S CONSTANT 𝑁. is the number of atoms in 12g of Carbon-12
𝑵𝑨 = 𝟔. 𝟎𝟐 × 𝟏𝟎𝟐𝟑
MOLES [MOL] The amount of substance containing 𝑁. atoms.
0
(number of moles) 𝑛 = 0 (number of molecules/Avogadro’s constant)
!
IDEAL GAS 12
A gas obeying = constant
3
where P = pressure; V = volume; T = temperature
𝑷𝑽 = 𝑵𝒌𝑻 𝑷𝑽 = 𝒏𝑹𝑻
!+, !4
where Boltzmann’s Constant k = 1.38 × 10 𝐽𝐾 where Molar Gas Constant R = 8.31 𝐽 𝑘 !4 𝑚𝑜𝑙 !4
If Temperature of Gas is constant: If Volume of Gas is constant: If Pressure of Gas is constant:
1 𝑃∝𝑇 𝑉∝𝑇
𝑃∝
𝑉
KINETIC THEORY OF IDEAL • [Molecules in] Random Motion (gravity negligible)
GAS • NO intermolecular force between molecules (PE = 0)
• Collisions are instantaneous (time between collision >> time during collision)
• Molecules have negligible volume compared to volume of container
• Collisions are elastic (no KE loss/total KE conserved)
∵ no intermolecular force between moleucles
∴ PE = 0, Internal Energy = Kinetic Energy à Avg. KE ∝ T à IE ∝ T
