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
\( v_{av} = \dfrac{x_f - x_i}{t_f - t_i} =\dfrac{\Delta x}{\Delta t} \) vav is the average velocity (vector)
Δ x is the displacement(vector)
Δ t is the time elapsed
\( a_{av} = \dfrac{v_f - v_i}{t_f - t_i} =\dfrac{\Delta v}{\Delta t} \) aav is the average acceleartion (vector)
Δ v is the change in velocity (vector)
Δ t is the time elapsed
\( v_{av} = \dfrac{v_i + v_f}{2} \) vav is the average velocity (vector)
vi is the initial velocity (vector)
vf is the final velocity (vector)
\( v_{f} = v_{i} + a \Delta t \) vf is the final velocity (vector)
vi 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)
vi 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)
vf 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)
vf is the final velocity (vector)
vi is the initial velocity (vector)
\( v^2_f = v^2_i + 2 a \cdot \Delta x \) vf is the final velocity (vector)
vi is the initial velocity (vector)
Δ x is the displacement (vector)
a is the acceleration (vector)

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)

Kinematics (Quantitative Description of Projectile Motion)



Example 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.
\( \Delta x = |v_i|\cos(\theta) \Delta t \) 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 / s2

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)
\( F_g = m g \) Fg is the weight (vector)
m is the mass
g is the acceleration (near the Earth) due to gravitation (vector)
\( | F_f | = \mu | F_N | \) 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)
\( p = m v \) 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
\( a_c = \dfrac{v^2}{r} \) ac is the centripetal acceleration
v is the velocity
r is the radius
\( F_c = \dfrac{m v^2}{r} \) Fc 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
\( E_k = \dfrac{1}{2} m v^2 \) Ek is the kinetic energy
v is the velocity
m is the mass
\( E_p = m g h \) 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
\( E_t = E_k + E_p \) Et is the total energy
Ek is the kinetic energy
Ep 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
\( E_s = \dfrac{1}{2} k x^2 \) 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

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

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
\( g_r = \dfrac{G m}{r^2} \) 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
\( E_p = -\dfrac{G M m}{r} \) 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

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
q1 and q1 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
\( E_p = k \dfrac{q_1 q_2}{r} \) 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
\( V = k \dfrac{q}{r} \) 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
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
\( B = \dfrac{\mu _0 N I}{L} \) 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
\( F_m = q v B \sin(\theta) \) 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
\( F_m = I L B \sin(\theta) \) 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
\( F_m = \dfrac{ \mu _0 I_1 I_2 L }{2 \pi r} \) 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

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 × 108m/s)
n is the index of refraction of the medium
\( n_1 \sin \theta_1 = n_2 \sin \theta_2 \) 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
\( \theta_c = \sin^{-1}(\dfrac{n_2}{n_1}) \) 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)
\( \dfrac{1}{D_0} + \dfrac{1}{D_i} = \dfrac{1}{F} \) D0 is the distance to the object
Di is the distance to the image
F is the focal length

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
\( E_k = h f - \phi \) 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)
\( p = \dfrac{h}{\lambda} \) 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
\( R_s = R_1 + R_2+... \) Rs is the total resistance equivalent to several resistors in series (end to end)
R1 resistance of resistor 1
R2 resistance of resistor 2
\( \dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} ... \) Rp is the total resistance equivalent to several resistors in parallel (side by side)
R1 resistance of resistor 1
R2 resistance of resistor 2
\( C = \dfrac{\epsilon A}{d} \) 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
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