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Published byMonica Olafsen Modified over 5 years ago
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Equation relating speed, frequency, and wavelength of a wave
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𝑐= 𝑓𝜆
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Definition of PERIOD (T)
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Time taken for one complete oscillation (measured in seconds)
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Definition of FREQUENCY (f)
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Number of complete oscillations per second
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Equation relating frequency and period of an oscillation
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𝑓= 1 𝑇
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Equation for finding the frequency of the first harmonic for stationary waves on a string
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𝑓= 1 2𝑙 𝑇 𝜇
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Equation for the double slit experiment, relating fringe separation, slit spacing, distance from screen, and wavelength of light.
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𝑤= 𝜆𝐷 𝑠
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Equation for diffraction grating
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𝑑 𝑠𝑖𝑛𝜃= 𝑛𝜆
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Formula for refractive index of a substance
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𝑛= 𝑐 𝑐 s
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Law of Refraction
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𝑛 1 𝑠𝑖𝑛 𝜃 1 = 𝑛 2 𝑠𝑖𝑛 𝜃 2
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Critical Angle
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𝑠𝑖𝑛 𝜃 𝑐 = 𝑛 2 𝑛 1 for n1 > n2
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Moment of a Force
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Force × perpendicular distance from the pivot, Fd
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Word definition of velocity
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Rate of change of displacement
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Definition of velocity in symbols
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𝑣 = Δ𝑠 Δ𝑡
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Word definition of acceleration
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Rate of change of velocity
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Definition of acceleration in symbols
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𝑎 = Δ𝑣 Δ𝑡
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Equations of motion for uniform acceleration (the “suvat” equations)
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𝑣=𝑢+𝑎𝑡 𝑠= 𝑢+𝑣 2 𝑡 𝑣 2 = 𝑢 2 +2𝑎𝑠 𝑠=𝑢𝑡+ 1 2 𝑎 𝑡 2
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Equation relating force, mass, and acceleration
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𝐹= 𝑚𝑎
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Definition of momentum (p)
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momentum = mass × velocity p = mv
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Definition of impulse
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𝐹∆𝑡= ∆(𝑚𝑣
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Equation relating force, momentum, and time in words
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Force = rate of change of momentum
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Equation relating force, momentum, and time in symbols
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𝐹= 𝑚𝑣−𝑚𝑢 𝑡 or 𝐹= ∆𝑚𝑣 𝑡
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Equation relating work done, force, and distance
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𝑤= 𝐹𝑠 or 𝑤= 𝐹𝑠 𝑐𝑜𝑠 𝜃
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Equation for kinetic energy
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𝐸 𝑘 = 1 2 𝑚 𝑣 2
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Equation for gravitational potential energy
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∆ 𝐸 𝑝 = 𝑚𝑔∆ℎ
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Definition of POWER in words
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Power is the rate of conversion of energy
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Definition of POWER (P) in symbols
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𝑃= ∆𝑤 ∆𝑡
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Equation relating power, force, and velocity
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𝑃= 𝐹𝑣
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Definition of EFFICIENCY
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𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦= 𝑢𝑠𝑒𝑓𝑢𝑙 𝑝𝑜𝑤𝑒𝑟 𝑜𝑢𝑡𝑝𝑢𝑡 𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑤𝑒𝑟 𝑖𝑛𝑝𝑢𝑡
𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦= 𝑢𝑠𝑒𝑓𝑢𝑙 𝑝𝑜𝑤𝑒𝑟 𝑜𝑢𝑡𝑝𝑢𝑡 𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑤𝑒𝑟 𝑖𝑛𝑝𝑢𝑡 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦= 𝑢𝑠𝑒𝑓𝑢𝑙 𝑝𝑜𝑤𝑒𝑟 𝑜𝑢𝑡𝑝𝑢𝑡 𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑤𝑒𝑟 𝑖𝑛𝑝𝑢𝑡 × 100 %
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Definition of DENSITY
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𝜌= 𝑚 𝑣
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Hooke’s Law
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𝐹= 𝑘∆𝐿
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Young Modulus
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𝑡𝑒𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑒𝑠𝑠 𝑡𝑒𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑎𝑖𝑛 = 𝐹×𝐿 𝐴 × ∆𝐿
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Tensile Stress
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F A
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Tensile Stress
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Δ𝐿 L
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Equation for calculating energy stored in a stretched or compressed material obeying Hooke’s Law
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𝐸= 1 2 𝐹∆𝐿 𝐸 = 1 2 𝑘∆ 𝐿 2
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Equation for calculating energy stored per unit volume for a stretched or compressed material obeying Hooke’s Law
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½ stress × strain
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Definition of WEIGHT
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𝑊=𝑚𝑔
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Equation for energy of a photon
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𝐸=ℎ𝑓= ℎ𝑐 𝜆
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Photoelectric effect equation
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ℎ𝑓=𝜙+ 𝐸 𝑘(max
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de Broglie wavelength
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𝜆= ℎ 𝑝 = ℎ 𝑚𝑣
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Definition of Work Function
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𝜙 = the minimum amount of energy needed to release an electron from the surface of a metal
𝜙=ℎ𝑓0
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Definition of Stopping Potential
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Stopping potential, 𝑉𝑠 is the potential difference needed to stop the fastest moving electron in a photocell experiment Ek(max) = eVs
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Definition of Specific Charge
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Q m
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Equation relating current, charge, and time
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𝐼= ∆𝑄 ∆𝑡
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Equation relating p.d., work done, and charge
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𝑉= 𝑊 𝑄
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Definition of the VOLT
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1 joule per coulomb
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Equation relating p.d., current, and resistance
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𝑉= 𝐼𝑅
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Equation defining resistivity
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ρ= 𝑅𝐴 𝑙
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Equation for calculating total resistance of resistors in series
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𝑅 𝑇 = 𝑅 1 + 𝑅 2 + 𝑅 3 …
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Equation for calculating total resistance of resistors in parallel
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1 𝑅 𝑇 = 1 𝑅 𝑅 𝑅 3 +… or 𝑅 𝑇 = 𝑅 𝑅 𝑅 3 +… −1
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Three equations for electrical power in a circuit
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𝑃=𝐼𝑉= 𝐼 2 𝑅= 𝑉 2 𝑅
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Equation relating p.d. and current to the total energy transferred by a component in a time, t.
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𝐸=𝐼𝑡𝑉
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Definition of electromotive force (emf) in words and symbols
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amount of energy supplied per coulomb by a power source
𝜀= 𝐸 𝑄 units: volts
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Equation relating emf of a power supply, its internal resistance and the external resistance in a circuit
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𝜀=𝐼(𝑅+𝑟
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Equation relating emf of a power supply, its internal resistance, the current through the circuit, and the p.d. across the external components
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𝑉=𝜀−𝐼𝑟
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Equation defining angular speed
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𝜔= 𝜃 𝑡
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Equation relating angular speed to frequency of orbit
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𝜔= 2𝜋𝑓
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Equation relating angular speed to period of orbit
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𝜔= 2𝜋 𝑇
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Equation relating angular speed to linear velocity and radius of orbit
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𝜔= 𝑣 𝑟
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Equation for centripetal force
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𝐹= 𝑚𝑣 2 𝑟 =𝑚 𝜔 2 𝑟
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Equations for centripetal acceleration
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𝑎= 𝑣 2 𝑟 = 𝜔 2 𝑟
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Criteria for Simple Harmonic Motion (SHM)
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Acceleration is proportion to the displacement, and always directed in the opposite direction, towards the equilibrium position
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Equation relating acceleration and angular frequency in SHM
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a = -ω2x
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Equation for displacement in SHM
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x = A cos(ωt)
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Equation for speed in SHM
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𝑣=± 𝜔 𝐴 2 − 𝑥 2
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Equation for maximum speed in SHM
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𝑣 𝑚𝑎𝑥 =𝜔𝐴
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Equation for maximum acceleration in SHM
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𝑎 𝑚𝑎𝑥 = ω2A
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Equation for period of SHM in a mass-spring system
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𝑇=2𝜋 𝑚 𝑘
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Equation for period of SHM of a simple pendulum
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𝑇=2𝜋 𝑙 𝑔
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Definition of specific heat capacity
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Definition of specific latent heat of fusion
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Definition of specific latent heat of vaporisation
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Energy needed to change temperature of a substance
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𝑄=𝑚𝑐Δ𝜃
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Energy needed to change state of a substance
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𝑄=𝑚𝑙
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Gas Law with Boltzmann Constant
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𝑝𝑉=𝑁𝑘𝑇
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Gas Law with molar gas constant
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𝑝𝑉=𝑛𝑅𝑇
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Kinetic Theory Equation
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𝑝𝑉= 1 3 𝑁𝑚 𝑐 rms 2
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Kinetic Energy of a Gas Molecule
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1 2 𝑚 𝑐 rms 2 = 3 2 𝑘𝑇= 3𝑅𝑇 2 𝑁 A
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Relationship between Pressure, Temperature, and Volume
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𝑃 1 𝑉 1 𝑇 1 = 𝑃 2 𝑉 2 𝑇 2
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Gravitational force between two masses
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𝐹= 𝐺𝑚 1 𝑚 2 𝑟 2
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Word definition of gravitational field strength
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Force per unit mass
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Equation defining of gravitational field strength
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𝑔= F m
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magnitude of gravitational field strength in a radial field
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𝑔= GM 𝑟 2
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Work done in moving a mass in a gravitational field
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Δ𝑊=𝑚Δ𝑉
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Word definition of gravitational potential
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the work done per unit mass in bringing a point mass from infinity to a point in a gravitational field (unit: 𝐽𝑘𝑔−1)
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Equation for gravitational potential
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𝑉=− GM r
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Why is gravitational potential always negative?
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zero gravitational potential is defined as being as being at infinity, and since work has to be done to a mass to get it to infinity, gravitational potential is always negative
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Equation relating gravitational field strength and gravitational potential
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g=− Δ𝑉 Δ𝑟
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Equation for escape velocity
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𝑣 𝑒𝑠𝑐 = 2𝐺𝑀 𝑟
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Equation relating period of satellite orbit to radius of orbit
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𝑇 2 = 4 𝜋 2 𝐺𝑀 𝑟 3
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Equation for gravitational potential energy in a radial field
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𝐸 𝑝 = − 𝐺𝑚 1 𝑚 2 𝑟
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force between two point charges
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𝐹= 1 4𝜋 𝜀 𝑄 1 𝑄 2 𝑟 2
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Word definition of electric field strength
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Force per unit charge
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definition of electric field strength in symbols
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𝐸= 𝐹 𝑄
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Formula for electric field strength between two parallel plates
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𝐸= 𝑉 𝑑
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definition of uniform field
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Field strength and direction same at all points
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Work done in moving a charge in an electric field
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Δ𝑊=𝑄Δ𝑉
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Equation for field strength for a radial field
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𝐸= 1 4𝜋 𝜀 0 𝑄 𝑟 2
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Equation for electric potential
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𝑉= 1 4𝜋 𝜀 0 𝑄 𝑟
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Equation relating electric field strength and electric potential
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𝐸= ∆𝑉 ∆𝑟
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Equation for electric potential energy at a point in a radial field
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𝐸 𝑝 = 1 4𝜋 𝜀 𝑄 1 𝑄 2 𝑟
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Equation relating capacitance, charge, and voltage
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𝐶= 𝑄 𝑉
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Equation relating capacitance to area of plates, separation of plates, and permittivity of dielectric
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𝐶= 𝐴 𝜀 0 𝜀 𝑟 𝑑
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Energy stored in a capacitor
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𝐸= 1 2 𝑄𝑉 𝐸= 1 2 𝐶 𝑉 2 𝐸= 𝑄 2 𝐶
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Equations describing discharging a capacitor
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𝑄= 𝑄 0 𝑒 − 𝑡 𝑅𝐶 𝑉= 𝑉 0 𝑒 − 𝑡 𝑅𝐶 𝐼= 𝐼 0 𝑒 − 𝑡 𝑅𝐶
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Equations describing charging up a capacitor
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𝑄= 𝑄 0 (1−𝑒 − 𝑡 𝑅𝐶 ) 𝑉= 𝑉 0 (1−𝑒 − 𝑡 𝑅𝐶 ) 𝐼= 𝐼 0 𝑒 − 𝑡 𝑅𝐶
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Word definition of the time constant for a resistor-capacitor (RC) circuit
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Time taken for the charge or potential difference or current to fall to 1/e of its original value for a discharging capacitor
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Equation for calculating time constant for a discharging capacitor
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𝜏= 𝑅𝐶
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Time taken for a capacitor to discharge 99% of its charge or current or potential difference
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5 time constants
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Equations defining relative permittivity
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𝜀 𝑟 = 𝐶 𝐶 0 = 𝑄 𝑄 0 = 𝜀 1 𝜀 0
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