Friday, 10 February 2017

physics formulas in mechanics

Physics Formulas 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 is defined as force per unit area:
Pressure (P) = Force (F)
Area (A)

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

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