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Showing posts from August, 2019

What is rigid body?

A system of large number of particles in which the distance between any two particles remains fix throughout the motion is called rigid body.

Moment of inertia
Moment of inertia I is given by,
$$ I = \Sigma m_i r_i^2$$

If a force \(\vec{F}\) acts at a point, whose position vector is \(\vec{r}\); the torque due to force
$$\vec{\tau} = \vec{r} \times \vec{F}$$

Angular displacement
Angular displacement is given by, $$ \theta = \frac{s}{r} $$

Angular velocity
Angular velocity is given by,
$$\omega = \frac{d\theta}{dt}$$

Angular acceleration
Angular accceleration is given by,
$$\alpha = \frac{d\omega}{dt}$$
SI unit of angular acceleration is rad s-2. Its dimensional formula is [M0L0T-2].

Angular momentum
Angular momentum is given by $$\vec{L} = \vec{r} \times \vec{p}$$ Where \(\vec{p}\) is linear momentum of the particle and \(\vec{r}\) is position vector of the particle.

Relation between torque and angular momentum
Relation between torque and angular momentum is given $$\tau = \frac{d\vec{L}}{dt}$$


What is the ideal gas equation?

The equation of state of an ideal gas is given by,
PV = nRT
Where, n is the number of moles of the gas and R is the gas constant for one mole of the gas.

The gas law
Boyle's law
If \(\mu\) and T are constant then idael gas equation becomes, $$PV = Constant $$ or $$ P \propto \frac{1}{V} $$ This is the Boyle's law.

Charle's law
If \(\mu\) and P are constant then idael gas equation becomes,
$$ V \propto T $$ This is the Charle's law.

Gay lussac's law
If \(\mu\) and V are constant then idael gas equation becomes,
$$ P \propto T $$ This is the Gay lussac's law.

Specific heat capacity
Specific heat capacity is given by,
$$ s = \frac{S}{m}$$
Where, S is heat capacity and $latex m$ is the mass of substance.
The unit of specific heat capacity is J kg-1 k-1

Degrees of freedom

Number of degrees of freedom of a system is given by following,
N = 3A - R
A is the number of particles in the system and R is the number of independent relations among the particles.

For mono atomic gases, the…

What are the different types of waves?

Basically waves can be three types:

Mechanical waves
Electromagnetic waves
Matter waves

Mechanical waves
Waves which can be produced and propagated only in a material medium are known as mechanical waves.
Water waves, sound waves, waves on string, seismic waves etc. are the example of mechanical waves.
The propagation of mechanical wave depends on the elasticity and inertia of the medium. Thus, these waves are known as elastic waves.

Mechanical waves are two types: Transverse waves and longitudinal waves.
Transverse waves
Waves on the water surface, light waves, wave generated on the string etc are the examples of transverse waves.
Longitudinal wave
Sound wave propagated in air is the example of longitudinal waves.
Electromagnetic waves
Those waves which requires no material medium for their production and propagation, this means it propagates in vacuum. Such waves are called electromagnetic waves.
Visible light, ultraviolet light, radio waves, microwaves, X-rays etc are the examples of electromag…