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Most Important And Most Frequently Used Formulas in Physics (2)

Physics Problem Solving For High School - Formula, Definition and explanations - Some of the most important and most frequently used formulas in physics lessons at our school are presented and explained below. We look forward to helping you solve physics problems in school.
Most Important And Most Frequently Used Formulas in Physics (2)
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
\[E_s = \frac{1}{2} k x^2\]
  • 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
\[T_s = 2\pi \sqrt{\frac{m}{k}}\]
  • Ts is the time period of motion
  • k is the spring constant
  • m is the mass attached to the spring
\[T_p = 2\pi \sqrt{\frac{L}{g}}\]
  • 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
\[= G \frac{m_1 m_2}{r^2}\]
  • 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
\[g_r = \frac{G m}{r^2}\]
  • $g_r$ 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
\[E_p = -\frac{G M m}{r}\]
  • 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
\[v = \sqrt{ \frac{G M}{r} }\]
  • 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
\[T = \sqrt{ \frac{4\pi^2r^3}{G M} }\]
  • 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
\[v = \frac{2\pi r }{T}\]
  • 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
\[F = k \frac{q_1 q_2}{r^2}\]
  • 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
\[E = k \frac{q}{r^2}\]
  • 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
\[E_p = k \frac{q_1 q_2}{r}\]
  • 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
\[V = k \frac{q}{r}\]
  • V is the electric potential
  • k is a constant
  • q is the charge
  • r is the distance from the charge q
\[E = \frac{V}{d}\]
  • 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
\[= \frac{\mu _0 I}{2 \pi r}\]
  • B is magnetic field due to current I in a long conductor of length L
  • μo 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
\[B = \frac{\mu _0 N I}{L}\]
  • B is the magnetic field (in the center of the solenoid) due to current I in a solenoid of length L
  • μo 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
\[F_m = \frac{ \mu _0 I_1 I_2 L }{2 \pi r}\]
  • Fm is the magnetic force of attraction or repulsion between two parallel wires
  • μo 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
\[f = \frac{1}{T}\]
  • f is the wave frequency
  • T is the period of the wave

Optics
Formula, Definition and explanations
\[v = \frac{c}{n}\]
  • 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
\[\theta_c = \sin^{-1}(\frac{n_2}{n_1})\]
  • 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)
\[\frac{1}{D_o} + \frac{1}{D_i} = \frac{1}{F}\]
  • Do 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)
\[p = \frac{h}{\lambda}\]
  • 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
\[P = I^2 R = \frac{V^2}{R} = I V\]
  • 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
\[\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} ...\]
  • Rp is the total resistance equivalent to several resistors in parallel (side by side)
  • R1 resistance of resistor 1
  • R2 resistance of resistor 2
\[C = \frac{\epsilon A}{d}\]
  • 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
\[W = \frac{C V^2}{2}\]
  • W is the total energy stored in a capacitor
  • C is the capacitance
  • V is the voltage across the capacitor
See also:
Most Important And Most Frequently Used Formulas in Physics (1)