A Comprehensive List of All the Physics Formulas (Part 1)

Learning physics is all about applying concepts to solve problems. This article provides a comprehensive physics formulas list, that will act as a ready reference, when you are solving physics problems. You can even use this list, for a quick revision before an exam.

Physics Science School Education Blackboard

Physics is the most fundamental of all sciences. It is also one of the toughest sciences to master. Learning physics is basically studying the fundamental laws that govern our universe. I would say that there is a lot more to ascertain than just remember and mug up the physics formulas. Try to understand what a formula says and means, and what physical relation it expounds. If you understand the physical concepts underlying those formulas, deriving them or remembering them is easy. This Buzzle article lists some physics formulas that you would need in solving basic physics problems.

Physics Formulas

  • Mechanics
  • Friction
  • Moment of Inertia
  • Newtonian Gravity
  • Projectile Motion
  • Simple Pendulum
  • Electricity
  • Thermodynamics
  • Electromagnetism
  • Optics
  • Quantum Physics

Derive all these formulas once, before you start using them. Study physics and look at it as an opportunity to appreciate the underlying beauty of nature, expressed through natural laws. Physics help is provided here in the form of ready to use formulas. Physics has a reputation for being difficult and to some extent that’s true, due to the mathematics involved. If you don’t wish to think on your own and apply basic physics principles, solving physics problems is always going to be tough. Our physics formulas list is aimed at helping you out in solving problems. The joy of having solved a physics problem on your own, is worth all the effort! Understanding physics concepts challenges your imagination and thinking potential, wherein, if you visualize a problem, then you can come up with a solution. So here is the promised list which will help you out.

Mechanics

Mechanics is the oldest branch of physics. Mechanics deals with all kinds and complexities of motion. It includes various techniques, which can simplify the solution of a mechanical problem.

Motion in One Dimension
The formulas for motion in one dimension (Also called Kinematical equations of motion) are as follows. (Here ‘u’ is initial velocity, ‘v’ is final velocity, ‘a’ is acceleration and t is time):
s = ut + ½ at2
v = u + at
v2 = u2 + 2as
vav (Average Velocity) = (v+u)/2

Momentum, Force and Impulse
Formulas for momentum, impulse and force concerning a particle moving in 3 dimensions are as follows (Here force, momentum and velocity are vectors ):
Momentum is the product of mass and velocity of a body. Momentum is calculate using the formula: P = m (mass) x v (velocity)
Force can defined as something which causes a change in momentum of a body. Force is given by the celebrated newton’s law of motion: F = m (mass) x a (acceleration)
Impulse is a large force applied in a very short time period. The strike of a hammer is an impulse. Impulse is given by I = m(v-u)

Pressure
Pressure is defined as force per unit area:

Pressure (P) = Force (F)
Area (A)

Density
Density is the mass contained in a body per unit volume.

The formula for density is:
Density (D) = Mass(M)
Volume (V)

Angular Momentum
Angular momentum is an analogous quantity to linear momentum in which the body is undergoing rotational motion. The formula for angular momentum (J) is given by:

J = r x p
where J denotes angular momentum, r is radius vector and p is linear momentum.

Torque
Torque can be defined as moment of force. Torque causes rotational motion. The formula for torque is: τ = r x F, where τ is torque, r is the radius vector and F is linear force.

Circular Motion
The formulas for circular motion of an object of mass ‘m’ moving in a circle of radius ‘r’ at a tangential velocity ‘v’ are as follows:

Centripetal force (F) = mv2
r
Centripetal Acceleration (a) = v2
r

Center of Mass
General Formula for Center of mass of a rigid body is :
R = ΣNi = 1 miri
ΣNi = 1mi

where R is the position vector for center of mass, r is the generic position vector for all the particles of the object and N is the total number of particles.

Reduced Mass for two Interacting Bodies
The physics formula for reduced mass (μ) is :
μ = m1m2
m1 + m2
where m1 is mass of the first body, m2 is the mass of the second body.

Work and Energy
Formulas for work and energy in case of one dimensional motion are as follows:

W (Work Done) = F (Force) x D (Displacement)

Energy can be broadly classified into two types, Potential Energy and Kinetic Energy. In case of gravitational force, the potential energy is given by

P.E.(Gravitational) = m (Mass) x g (Acceleration due to Gravity) x h (Height)

The transitional kinetic energy is given by ½ m (mass) x v2(velocity squared)

Power
Power is, work done per unit time. The formula for power is given as
Power (P) = V2
R =I2R
where P=power, W = Work, t = time.

Friction

Friction can be classified to be of two kinds : Static friction and dynamic friction.

Static Friction: Static friction is characterized by a coefficient of static friction μ . Coefficient of static friction is defined as the ratio of applied tangential force (F) which can induce sliding, to the normal force between surfaces in contact with each other. The formula to calculate this static coefficient is as follows:

μ = Applied Tangential Force (F)
Normal Force(N)

The amount of force required to slide a solid resting on flat surface depends on the co efficient of static friction and is given by the formula:

FHorizontal = μ x M(Mass of solid) x g (acceleration)

Dynamic Friction:
Dynamic friction is also characterized by the same coefficient of friction as static friction and therefore formula for calculating coefficient of dynamic friction is also the same as above. Only the dynamic friction coefficient is generally lower than the static one as the applied force required to overcome normal force is lesser.

Moment of Inertia

Here are some formulas for Moments of Inertia of different objects. (M stands for mass, R for radius and L for length):

Object Axis Moment of Inertia
Disk Axis parallel to disc, passing through the center MR2/2
Disk Axis passing through the center and perpendicular to disc MR2/2
Thin Rod Axis perpendicular to the Rod and passing through center ML2/12
Solid Sphere Axis passing through the center 2MR2/5
Solid Shell Axis passing through the center 2MR2/3

Newtonian Gravity

Here are some important formulas, related to Newtonian Gravity:
Newton’s Law of universal Gravitation:

Fg = Gm1m2
r2

where

  • m1, m2 are the masses of two bodies
  • G is the universal gravitational constant which has a value of 6.67300 × 10-11 m3 kg-1 s-2
  • r is distance between the two bodies

Formula for escape velocity (vesc) = (2GM / R)1/2where,

  • M is mass of central gravitating body
  • R is radius of the central body

Projectile Motion

Here are two important formulas related to projectile motion:
(v = velocity of particle, v0 = initial velocity, g is acceleration due to gravity, θ is angle of projection, h is maximum height and l is the range of the projectile.)

Maximum height of projectile (h) = v0 2sin2θ
2g

Horizontal range of projectile (l) = v0 2sin 2θ / g

Simple Pendulum

The physics formula for the period of a simple pendulum (T) = 2π √(l/g) where

  • l is the length of the pendulum
  • g is acceleration due to gravity

Conical Pendulum
The Period of a conical pendulum (T) = 2π √(lcosθ/g)
where

  • l is the length of the pendulum
  • g is acceleration due to gravity
  • Half angle of the conical pendulum

Electricity

Here are some formulas related to electricity.

Ohm’s Law

Ohm’s law gives a relation between the voltage applied a current flowing across a solid conductor:

V (Voltage) = I (Current) x R (Resistance)

Power
In case of a closed electrical circuit with applied voltage V and resistance R, through which current I is flowing,
Power (P) = V2
R

= I2R. . . (because V = IR, Ohm’s Law)

Kirchoff’s Voltage Law
For every loop in an electrical circuit:

ΣiVi = 0
where Vi are all the voltages applied across the circuit.

Kirchoff’s Current Law
At every node of an electrical circuit:

ΣiIi = 0
where Ii are all the currents flowing towards or away from the node in the circuit.

Resistance

The physics formulas for equivalent resistance in case of parallel and series combination are as follows:
Resistances R1, R2, R3 in series:

Req = R1 + R2 + R3

Resistances R1 and R2 in parallel:
Req = R1R2
R1 + R2

For n number of resistors, R1, R2…Rn, the formula will be:

1/Req = 1/R1 + 1/R2 + 1/R3…+ 1/Rn

Capacitors

A capacitor stores electrical energy, when placed in an electric field. A typical capacitor consists of two conductors separated by a dielectric or insulating material. Here are the most important formulas related to capacitors. Unit of capacitance is Farad (F) and its values are generally specified in mF (micro Farad = 10 -6 F).

Capacitance (C) = Q / V

Energy Stored in a Capacitor (Ecap) = 1/2 CV2 = 1/2 (Q2 / C) = 1/2 (QV)

Current Flowing Through a Capacitor I = C (dV / dt)

Equivalent capacitance for ‘n’ capacitors connected in parallel:

Ceq (Parallel) = C1 + C2 + C3…+ Cn = Σi=1 to n Ci

Equivalent capacitance for ‘n’ capacitors in series:

1 / Ceq (Series) = 1 / C1 + 1 / C2…+ 1 / Cn = Σi=1 to n (1 / Ci)

Here

  • C is the capacitance
  • Q is the charge stored on each conductor in the capacitor
  • V is the potential difference across the capacitor

Parallel Plate Capacitor Formula:

C = kε0 (A/d)

Where

  • k = dielectric constant (k = 1 in vacuum)
  • ε0 = Permittivity of Free Space (= 8.85 × 10-12 C2 / Nm2)
  • A = Plate Area (in square meters)
  • d = Plate Separation (in meters)

Cylinrical Capacitor Formula:

C = 2π kε0 [L / ln(b / a)]

Where

  • k = dielectric constant (k = 1 in vacuum)
  • ε0 = Permittivity of Free Space (= 8.85 × 10-12 C2 / Nm2)
  • L = Capacitor Length
  • a = Inner conductor radius
  • b = Outer conductor radius

Spherical Capacitor Formula:

C = 4π kε0 [(ab)/(b-a)]

Where

  • k = dielectric constant (k = 1 in vacuum)
  • ε0 = Permittivity of Free Space (= 8.85 × 10-12 C2 / Nm2)
  • a = Inner conductor radius
  • b = Outer conductor radius

 

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