Physics Formulas Reference
Some of the most important and frequently used formulas in physics are prsented and explained below.
Kinematics (Quantitative Description of Motion)
| Formula | Definition and explanations |
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s_{av} = \dfrac{d}{\Delta t}
| sav is the average speed (scalar)
d is the distance
Δ t is the time elapsed
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v_{av} = \dfrac{x_f - x_i}{t_f - t_i} =\dfrac{\Delta x}{\Delta t}
| vav is the average velocity (vector)
Δ x is the displacement(vector)
Δ t is the time elapsed
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a_{av} = \dfrac{v_f - v_i}{t_f - t_i} =\dfrac{\Delta v}{\Delta t}
| aav is the average acceleartion (vector)
Δ v is the change in velocity (vector)
Δ t is the time elapsed
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v_{av} = \dfrac{v_i + v_f}{2}
| vav is the average velocity (vector)
vi is the initial velocity (vector)
vf is the final velocity (vector)
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v_{f} = v_{i} + a \Delta t
| vf is the final velocity (vector)
vi is the initial velocity (vector)
a is the acceleration (vector)
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\Delta x = v_i \Delta t + \dfrac{1}{2} a (\Delta t)^2
| Δ x is the displacement (vector)
vi is the initial velocity (vector)
a is the acceleration (vector)
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\Delta x = v_f \Delta t - \dfrac{1}{2} a (\Delta t)^2
| Δ x is the displacement (vector)
vf is the final velocity (vector)
a is the acceleration (vector)
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\Delta x = \dfrac{v_f+v_i}{2} \Delta t
| Δ x is the displacement (vector)
vf is the final velocity (vector)
vi is the initial velocity (vector)
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v^2_f = v^2_i + 2 a \cdot \Delta x
| vf is the final velocity (vector)
vi is the initial velocity (vector)
Δ x is the displacement (vector)
a is the acceleration (vector)
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Relative Velocity
| Formula | Definition and explanations |
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v_{AC} = v_{AB}+v_{BC}
| vAC is the velocity of A with respect to C (vector)
vAB is the velocity of A with respect to B (vector)
vBC is the velocity of B with respect to C (vector)
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Kinematics (Quantitative Description of Projectile Motion)
| Formula | Definition and explanations |
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v_{ix} = |v_i|\cos(\theta) \\ v_{iy} = |v_i|\sin(\theta)
| vi is the initial velocity (vector)
vix is the component of the initial velocity along the horizontal direction x (scalar)
viy is the component of the initial velocity along the vertical direction y (scalar)
θ is the initial angle that vi makes with the horizontal.
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\Delta x = |v_i|\cos(\theta) \Delta t
| Δx is the displacement along the horizontal direction x
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\Delta y = |v_i|\sin(\theta) \Delta t - \dfrac{1}{2} g (\Delta t)^2
| Δy is the displacement along the vertical direction y
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R = \dfrac{v^2_i \sin(2\theta)}{g}
| R is the range or horizontal distance travelled when the projectile hits the ground
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T = \dfrac{2 v_i \sin(\theta)}{g}
| T is total time to hit the ground
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H = \dfrac{v^2_i \sin^2(\theta)}{2 g}
| H maximum height reached above the ground
g = 9.8 m / s2
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Dynamics (Forces and Momentum)
| Formula | Definition and explanations |
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F = m a
| F is the net force (vector)
m is the mass
a is the acceleration (vector)
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F_g = m g
| Fg is the weight (vector)
m is the mass
g is the acceleration (near the Earth) due to gravitation (vector)
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| F_f | = \mu | F_N |
| Ff is the force of friction (vector)
μ is the coefficient of friction (μ may be μk kinetic coefficient or μs static coefficient of friction)
FN is the normal (to the surface) force (vector)
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p = m v
| p is the momentum (vector)
m is the mass
v is the velocity (vector)
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\Delta p = F \Delta t
| Δ p is the change in momentum (vector)
F is the applied force (vector)
Δ t is the elapsed time
(F Δ t) is called impulse (vector)
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Circular Motion
| Formula | Definition and explanations |
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a_c = \dfrac{v^2}{r}
| ac is the centripetal acceleration
v is the velocity
r is the radius
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F_c = \dfrac{m v^2}{r}
| Fc is the centripetal force
v is the velocity
m is the mass
r is the radius
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v = \dfrac{2 \pi r}{T}
| v is the velocity
r is the radius
T is the period (time for one complete revolution)
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Work, Potential and Kinetic Energies
| Formula | Definition and explanations |
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W = F d \cos(\theta)
| W is the work done by the force F
F is the applied force (constant)
d is the distance
θ is the angle between F and the direction of motion
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E_k = \dfrac{1}{2} m v^2
| Ek is the kinetic energy
v is the velocity
m is the mass
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E_p = m g h
| Ep is the potential energy of an object close to the surface of Earth
m is the mass of the object
h is the height of the object with respect to some refernce (ground for example)
g = 9.8 m/s2
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E_t = E_k + E_p
| Et is the total energy
Ek is the kinetic energy
Ep is the potential energy
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Springs, Hooke's Law and Potential Energy
| Formula | Definition and explanations |
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F_s = k x
| F is the force applied to compress or stretch a spring
k is the spring constant
x is the length of extension or compression of the spring
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E_s = \dfrac{1}{2} k x^2
| Es is the potential energy stored in a spring when compressed or extended
k is the spring constant
x is the length of extension or compression of the spring
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Period of Simple Harmonic Motions
| Formula | Definition and explanations |
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T_s = 2\pi \sqrt{\dfrac{m}{k}}
| Ts is the time period of motion
k is the spring constant
m is the mass attached to the spring
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T_p = 2\pi \sqrt{\dfrac{L}{g}}
| Ep is the time period of motion
L is the length of the pendilum
g is the acceleration due to gravity
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Gravitational Fields and Forces
| Formula | Definition and explanations |
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F = G \dfrac{m_1 m_2}{r^2}
| F is force of attraction
G is the universal gravitational constant
m1 and m1 are the masses of the two objects attracting each other
r is the distance separating the centers of the two objects
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g_r = \dfrac{G m}{r^2}
| gr gravitational field intensity at a distance r
G is the universal gravitational constant
m is the mass
r is the distance (from mass m) where the field is measured
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E_p = -\dfrac{G M m}{r}
| Ep gravitational potential energy of mass m
G is the universal gravitational constant
G is the mass of the attracting body
m is the mass being attracted
r is the distance separating the centers of the masses M and m
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Satelite motion, orbital speed, period and radius
| Formula | Definition and explanations |
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v = \sqrt{ \dfrac{G M}{r} }
| v is the orbital speed of the satellite
G is the universal gravitational constant
M is the mass of the attracting body (Earth for example)
r is the distance from the center of mass M to the position of the satellite
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T = \sqrt{ \dfrac{4\pi^2r^3}{G M} }
| T is the orbital period of the satellite
G is the universal gravitational constant
m is the mass
r is the distance from the center of mass M to the the position of the satellite
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v = \dfrac{2\pi r }{T}
| v is the orbital speed of the satellite
r is the distance from the center of mass M to the the position of the satellite
T is the orbital period of the satellite
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Electric forces, fields and potentials
| Formula | Definition and explanations |
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F = k \dfrac{q_1 q_2}{r^2}
| F is the electric force
k is a constant
q1 and q1 are the charges attracting or repulsing each other
r is the distance separating the two charges
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F = q E
| F is the electric force
q is the charge
E is the eletcric field
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E = k \dfrac{q}{r^2}
| E is the electric field due charge q
k is a constant
q is the charge
r is the distance from the charge q where E is being calculated
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E_p = k \dfrac{q_1 q_2}{r}
| Ep is the electric potential energy for a system of two charges
k is a constant
q1 and q1 are the charges
r is the distance separating the two charges
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V = k \dfrac{q}{r}
| V is the electric potential
k is a constant
q is the charge
r is the distance from the charge q
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E = \dfrac{V}{d}
| E is the electric field between two large, oppositely charged, conducting parallel plates
V is the electric potential difference between the plates
d is the distance separating the two plates
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Magnetic fields and forces
| Formula | Definition and explanations |
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B = \dfrac{\mu _0 I}{2 \pi r}
| B is magnetic field due to current I in a long conductor of length L
μ0 is permeability in vacuum
I the current in the conductor
L is the length of the conductor
r is the distance from the conductor to where the field B is calculated
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B = \dfrac{\mu _0 N I}{L}
| B is the magnetic field (in the center of the solenoid) due to current I in a solenoid of length L
μ0 is permeability in vacuum
I the current in the solenoid
L is the length of the solenoid
N is the number of turns of the solenoid
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F_m = q v B \sin(\theta)
| Fm is the magnetic force (due to B) on a charge q moving at a velocity v
B the magnetic field
θ is the angle between B and the direction of motion of q
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F_m = I L B \sin(\theta)
| Fm is the magnetic force (due to B) on a wire with current I and length L
B the magnetic field
θ is the angle between B and the wire
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F_m = \dfrac{ \mu _0 I_1 I_2 L }{2 \pi r}
| Fm is the magnetic force of attraction or repulsion between two parallel wires
μ0 is permeability in vacuum
I1 and I2 are the currents in the two wires
L is the common length between the two wires
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Waves
| Formula | Definition and explanations |
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v = \lambda f
| v is the wave velocity
λ is the wavelength
f is the frequency
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f = \dfrac{1}{T}
| f is the wave frequency
T is the period of the wave
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Optics
| Formula | Definition and explanations |
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v = \dfrac{c}{n}
| v is the velocity of light in a medium of index n
c is speed of light in vacuum ( = 3.0 × 108m/s)
n is the index of refraction of the medium
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n_1 \sin \theta_1 = n_2 \sin \theta_2
| n1 is the index of refraction of medium 1
n2 is the index of refraction of medium 2
θ1 is the angle of incidence in medium 1
θ2 is the angle of refraction in medium 2
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\theta_c = \sin^{-1}(\dfrac{n_2}{n_1})
| θc is the critical angle such that when the angle of incidence is bigger that θc all light is reflected to medium 1
n1 is the index of refraction of medium 1 (medium of incidence)
n2 is the index of refraction of medium 2 (medium of refraction)
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\dfrac{1}{D_0} + \dfrac{1}{D_i} = \dfrac{1}{F}
| D0 is the distance to the object
Di is the distance to the image
F is the focal length
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Photoelectric Effects
| Formula | Definition and explanations |
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E = h f
| E is the energy of the photon
h is Plank's constant
f is the wave frequency of the photon
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E_k = h f - \phi
| Ek is the kinetic energy
h is Plank's constant
f is the wave frequency of the photon
φ is the work function of the metal (minimum work required to extract an electron)
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p = \dfrac{h}{\lambda}
| p is the momentum of the photon
h is Plank's constant
λ is the photon wavelength
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DC Circuits
| Formula | Definition and explanations |
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V = R I
| V is the voltage across a resistor
R is the resistance of the resistor
I is the current through the resistor
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P = I^2 R = \dfrac{V^2}{R} = I V
| P is the power dissipated as heat into a resistor
I is current through the resistor
R is the resistance of the resistor
V is the voltage across the resistor
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R_s = R_1 + R_2+...
| Rs is the total resistance equivalent to several resistors in series (end to end)
R1 resistance of resistor 1
R2 resistance of resistor 2
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\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} ...
| Rp is the total resistance equivalent to several resistors in parallel (side by side)
R1 resistance of resistor 1
R2 resistance of resistor 2
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C = \dfrac{\epsilon A}{d}
| C is the capacitance of a capacitor made up of two parallel plates
ε is the permittivity of the dielectric inside the two plates
A is the common area of the two plates
d is the distance between the two plates
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Q = C V
| Q is the total charge in a capacitor made up of two parallel plates
C is the capacitance
V is the voltage across the capacitor
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W = \dfrac{C V^2}{2}
| W is the total energy stored in a capacitor
C is the capacitance
V is the voltage across the capacitor
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