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}
 s_{av} is the average speed (scalar) d is the distance Δ t is the time elapsed

v_{av} = \dfrac{x_f  x_i}{t_f  t_i} =\dfrac{\Delta x}{\Delta t}
 v_{av} is the average velocity (vector) Δ x is the displacement(vector) Δ t is the time elapsed

a_{av} = \dfrac{v_f  v_i}{t_f  t_i} =\dfrac{\Delta v}{\Delta t}
 a_{av} is the average acceleartion (vector) Δ v is the change in velocity (vector) Δ t is the time elapsed

v_{av} = \dfrac{v_i + v_f}{2}
 v_{av} is the average velocity (vector) v_{i} is the initial velocity (vector) v_{f} is the final velocity (vector)

v_{f} = v_{i} + a \Delta t
 v_{f} is the final velocity (vector) v_{i} is the initial velocity (vector) a is the acceleration (vector)

\Delta x = v_i \Delta t + \dfrac{1}{2} a (\Delta t)^2
 Δ x is the displacement (vector) v_{i} is the initial velocity (vector) a is the acceleration (vector)

\Delta x = v_f \Delta t  \dfrac{1}{2} a (\Delta t)^2
 Δ x is the displacement (vector) v_{f} is the final velocity (vector) a is the acceleration (vector)

\Delta x = \dfrac{v_f+v_i}{2} \Delta t
 Δ x is the displacement (vector) v_{f} is the final velocity (vector) v_{i} is the initial velocity (vector)

v^2_f = v^2_i + 2 a \cdot \Delta x
 v_{f} is the final velocity (vector) v_{i} is the initial velocity (vector) Δ x is the displacement (vector) a is the acceleration (vector)

Relative Velocity
Formula  Definition and explanations 
v_{AC} = v_{AB}+v_{BC}
 v_{AC} is the velocity of A with respect to C (vector) v_{AB} is the velocity of A with respect to B (vector) v_{BC} is the velocity of B with respect to C (vector)

Kinematics (Quantitative Description of Projectile Motion)
Formula  Definition and explanations 
v_{ix} = v_i\cos(\theta) \\ v_{iy} = v_i\sin(\theta)
 v_{i} is the initial velocity (vector) v_{ix} is the component of the initial velocity along the horizontal direction x (scalar) v_{iy} is the component of the initial velocity along the vertical direction y (scalar) θ is the initial angle that v_{i} makes with the horizontal.

\Delta x = v_i\cos(\theta) \Delta t
 Δx is the displacement along the horizontal direction x

\Delta y = v_i\sin(\theta) \Delta t  \dfrac{1}{2} g (\Delta t)^2
 Δy is the displacement along the vertical direction y

R = \dfrac{v^2_i \sin(2\theta)}{g}
 R is the range or horizontal distance travelled when the projectile hits the ground

T = \dfrac{2 v_i \sin(\theta)}{g}
 T is total time to hit the ground

H = \dfrac{v^2_i \sin^2(\theta)}{2 g}
 H maximum height reached above the ground g = 9.8 m / s^{2}

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)

F_g = m g
 F_{g} is the weight (vector) m is the mass g is the acceleration (near the Earth) due to gravitation (vector)

 F_f  = \mu  F_N 
 F_{f} is the force of friction (vector) μ is the coefficient of friction (μ may be μ_{k} kinetic coefficient or μ_{s} static coefficient of friction) F_{N} is the normal (to the surface) force (vector)

p = m v
 p is the momentum (vector) m is the mass v is the velocity (vector)

\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)

Circular Motion
Formula  Definition and explanations 
a_c = \dfrac{v^2}{r}
 a_{c} is the centripetal acceleration v is the velocity r is the radius

F_c = \dfrac{m v^2}{r}
 F_{c} is the centripetal force v is the velocity m is the mass r is the radius

v = \dfrac{2 \pi r}{T}
 v is the velocity r is the radius T is the period (time for one complete revolution)

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

E_k = \dfrac{1}{2} m v^2
 E_{k} is the kinetic energy v is the velocity m is the mass

E_p = m g h
 E_{p} 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/s^{2}

E_t = E_k + E_p
 E_{t} is the total energy E_{k} is the kinetic energy E_{p} is the potential energy

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

E_s = \dfrac{1}{2} k x^2
 E_{s} 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

Period of Simple Harmonic Motions
Formula  Definition and explanations 
T_s = 2\pi \sqrt{\dfrac{m}{k}}
 T_{s} is the time period of motion k is the spring constant m is the mass attached to the spring

T_p = 2\pi \sqrt{\dfrac{L}{g}}
 E_{p} is the time period of motion L is the length of the pendilum g is the acceleration due to gravity

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 m_{1} and m_{1} are the masses of the two objects attracting each other r is the distance separating the centers of the two objects

g_r = \dfrac{G m}{r^2}
 g_{r} 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

E_p = \dfrac{G M m}{r}
 E_{p} 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

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

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

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

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 q_{1} and q_{1} are the charges attracting or repulsing each other r is the distance separating the two charges

F = q E
 F is the electric force q is the charge E is the eletcric field

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

E_p = k \dfrac{q_1 q_2}{r}
 E_{p} is the electric potential energy for a system of two charges k is a constant q_{1} and q_{1} are the charges r is the distance separating the two charges

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

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

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 μ_{0} 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

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 μ_{0} 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

F_m = q v B \sin(\theta)
 F_{m} 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

F_m = I L B \sin(\theta)
 F_{m} 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

F_m = \dfrac{ \mu _0 I_1 I_2 L }{2 \pi r}
 F_{m} is the magnetic force of attraction or repulsion between two parallel wires μ_{0} is permeability in vacuum I_{1} and I_{2} are the currents in the two wires L is the common length between the two wires

Waves
Formula  Definition and explanations 
v = \lambda f
 v is the wave velocity λ is the wavelength f is the frequency

f = \dfrac{1}{T}
 f is the wave frequency T is the period of the wave

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 × 10^{8}m/s) n is the index of refraction of the medium

n_1 \sin \theta_1 = n_2 \sin \theta_2
 n_{1} is the index of refraction of medium 1 n_{2} is the index of refraction of medium 2 θ_{1} is the angle of incidence in medium 1 θ_{2} is the angle of refraction in medium 2

\theta_c = \sin^{1}(\dfrac{n_2}{n_1})
 θ_{c} is the critical angle such that when the angle of incidence is bigger that θ_{c} all light is reflected to medium 1 n_{1} is the index of refraction of medium 1 (medium of incidence) n_{2} is the index of refraction of medium 2 (medium of refraction)

\dfrac{1}{D_0} + \dfrac{1}{D_i} = \dfrac{1}{F}
 D_{0} is the distance to the object D_{i} is the distance to the image F is the focal length

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

E_k = h f  \phi
 E_{k} 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)

p = \dfrac{h}{\lambda}
 p is the momentum of the photon h is Plank's constant λ is the photon wavelength

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

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

R_s = R_1 + R_2+...
 R_{s} is the total resistance equivalent to several resistors in series (end to end) R_{1} resistance of resistor 1 R_{2} resistance of resistor 2

\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} ...
 R_{p} is the total resistance equivalent to several resistors in parallel (side by side) R_{1} resistance of resistor 1 R_{2} resistance of resistor 2

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

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

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


