# Physics Equations- 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.