*MECHANICS FRICTION MOMENT OF INERTIA NEWTONIAN GRAVITY PROJECTILE MOTION SIMPLE PENDULUM ELECTRICITY*
Thermodynamics Electromagnet is 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

**Inductors**

An inductor is an
electrical component which resists the flow of electrons or electric current
through it. This property of inductance, in these devices, is caused by the
electromotive force, created by magnetic field induced in them. The unit of
inductance is Henry. Here are some important formulas associated with
inductors.

Energy Stored in
Inductor (Estored) = 1/2 (LI2)

Where, L is
inductance and I is the current flowing through the inductor.

Inductance of a
cylindrical air core Coil (L) = (m0KN2A / l)

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