Popular Pages

Share

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
>