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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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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