**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.**

*Mechanics*

*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):

'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

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

ALSO READ Electric lines of forces

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.

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

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