Physics in Depth

According to the postulates of Kinetic theory of gases, all matter is composed of atoms and molecules. When the substance is heated, the size of atoms/molecules remains unchanged but their space changes. As we increase the heat, the particles(atoms/molecules) vibrate more rapidly and takes up more space.  That is, more vibration is induced as we increase the heat increasing the average distance between the particles that results in expansion. We should remember that the size of the particles does not increase but the space between them does. To put it in a nut shell, the expansion is caused due to the vigorous vibration of the atoms/molecules induced by the application of heat. Image source   mansfieldct In this figure, we can see that the workers are trying to reconnect two wheels that have been separated due to the extreme cold. The oil-soaked rope is burnt next to the track which will cause the track to expand and thus reconnect.

Elasticity Structure of a material Matter is made up of molecules and atoms . The forces between different atoms are responsible for the structure of a molecule and the forces between the molecules are responsible for the structure of the material. Interatomic and intermolecular forces The force between two atoms are called the interatomic forces and the force that exists between two molecules are called the intermolecular forces . The potential energy curve is same for atoms and molecules as the force between two atoms has the same general nature as between the two molecules. This is shown in fig. below. The horizontal axis in potential energy curve represents the separation between the atoms / molecules. The zero of the potential energy is taken when the atoms are widely separated ( r = infinity ). As the separation is decreased from a larger value, the potential energy also decreases, becoming negative. This shows that the force between the atoms / m

Rotational Dynamics Rigid body A rigid body is defined as a solid body in which the particles are compactlt arranged so that the inter-particle distance is small and fixed and is not disturbed by any external forces applied. Such a body thus does not bend, stretch or vibrate when in motion. No ideal rigid-bodies exist! but the bodies, in which the small forces required to move them produce little or no bending, stretching etc., may be taken to be rigid . Translation and Rotation When a rigid body move as a whole in any direction, then the body is said to be in translatory motion . However, when a body turns around or rotate about a particular axis, then the body is said to be in rotational motion . A body may execute both translational and rotational motion simultaneously (at the same time) . Pure rotation : Consider the ceiling fan in your room. When it is on, each point on its body goes in a circle. Locate the centres of the circles

Equilibrium Equilibrium Image by Suraj Rai : Stone in Equilibrium Equilibrium is the state of rest or balance due to the equal action of opposing forces. Requirements of Equilibrium The vectors sum of all the external forces that act on the body must be zero. \(\vec{F_{net}}=0\) The vector sum of all external torques that act on the body, measured about any possible point, must also be zero. \(\vec{\tau_{net}}=0\) Moments When the steering wheel of a car is turned, the applied force is said to exert a moment , or turning-effect, about the axle attached to the wheel. The magnitude of the moment of a force F about a point O is defined as the product of the force F and the perpendicular distance OA from O to the line of action of F (fig.). Thus \(moment= \vec{F}\times OA \) The moment of a force is also called a torque(τ) .The magnitude of the moment is expressed in newton metre (Nm) where F is in Newton and OA is in metre. We shall take an an

Newton's universal law of gravitation The force of attraction between two given particles is inversely proportional to the square of their distance apart. \(\color{red}F=G\frac{Mm}{r^2}\) where G is a universal constant known as the gravitational constant . Dimension of G = [L 3 M -1 T -2 ] and \(G=6.67\times 10^{-11} Nm^2 kg^{-2}\) Newton's law of gravitation is also called the universal law as it is applicable for both celestial and terrestrial bodies in the universe. Inertial mass It is the measure of ability of body to oppose the change in the velocity(i.e., acceleration produced by an external force). From Newton's second law of motion, F=ma Inertial mass is , \(m=\frac{F}{a}\). This implies for a=1 m/s 2 , m=F. Thus, inertial mass of the body is equal to the magnitude of force to produce unit acceleration in a body. Gravitational mass It is defined by the Newton's universal law of gravitation. \(m=\frac{F\times R^2}{GM}\