Physics Volume-4 (Mechanics-IV)



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Contents

Centre of Mass


Description: Centre of mass is the point where the total mass of a system is concentrated.


Motion of Centre of Mass


Description: The motion of the center of mass follows the path determined by external forces on the system.


Linear Momentum of a System of Particles


Description: Linear momentum of a system is the vector sum of individual momenta of all particles.


Vector Product of Two Vectors -I


Description: The vector product of two vectors yields a vector perpendicular to both, with magnitude and direction.


Vector Product of Two Vectors -II


Description: The vector product results in a vector perpendicular to both original vectors, with specific direction.


Motion of Centre of Mass - II


Description: Motion of Center of Mass II: Describes mass movement in multi-body systems, focusing on interactions.


Angular Velocity & Linear Velocity


Description: Angular Velocity: Rotational speed around an axis. Linear Velocity: Straight-line speed of an object.


Torque & Angular Momentum


Description: Torque: Force causing rotation. Angular Momentum: Rotational equivalent of linear momentum, conserved in closed systems.


Equilibrium of a Rigid Body


Description: Equilibrium of a Rigid Body: Forces and torques balance, causing no linear or rotational motion.


Equilibrium of a Rigid Body - II


Description: Equilibrium of a Rigid Body II: Analyzes conditions for multiple forces and torques in complex systems.


Equilibrium of a Rigid Body - III


Description: Equilibrium of a rigid body means forces and torques balance out, preventing any motion or rotation.


Moment of Inertia - I


Description: Moment of inertia measures an object's resistance to rotational motion about a specific axis.


Moment of Inertia - II


Description: Moment of inertia depends on mass distribution relative to the rotation axis, affecting rotational dynamics.


Moment of Inertia - III


Description: Moment of inertia quantifies how mass distribution affects an object's resistance to rotational acceleration.


Torque and Angular Momentum - II


Description: Torque causes rotational motion, while angular momentum measures rotational motion’s quantity, depending on mass and velocity.


Theorems of Perpendicular and Parallel Axe - I


Description: Theorems of perpendicular and parallel axes relate to moments of inertia in rotating rigid bodies.


Theorems of Perpendicular and Parallel Axe - II


Description: These theorems extend to calculating moments of inertia about shifted axes in complex systems.


Kinematics of Rotational Motion about a Fixed Axis


Description: It studies the angular motion of objects around a fixed axis, involving angular velocity and acceleration.


Dynamics of Rotational Motion about a Fixed Axis - I


Description: It explores torque, angular momentum, and rotational energy in objects rotating about a fixed axis.


Dynamics of Rotational Motion about a Fixed Axis - II


Description: Focuses on equations of motion, involving torque, moment of inertia, and angular acceleration in rotational systems.


Angular Momentum about a Fixed Axis - I


Description: Angular momentum about a fixed axis depends on the moment of inertia and angular velocity of rotation.


Angular Momentum about a Fixed Axis - II


Description: Conservation of angular momentum states that it remains constant if no external torque acts on the system.


Angular Momentum about a Fixed Axis & Rolling Motion - I


Description: Combines rotational and translational motion, analyzing how angular momentum influences rolling without slipping.


Angular Momentum about a Fixed Axis & Rolling Motion - II


Description: Explores the conservation of angular momentum in rolling motion, focusing on the relationship between rotational and linear velocities.


Angular Momentum about a Fixed Axis & Rolling Motion - III


Description: Investigates energy distribution in rolling motion, balancing rotational kinetic energy and translational kinetic energy.


Angular Momentum about a Fixed Axis & Rolling Motion - IV


Description: Angular momentum about a fixed axis involves rotational inertia; rolling motion combines rotation and translation.


Angular Momentum about a Fixed Axis & Rolling Motion - V


Description: Angular momentum: conserved for a fixed axis; rolling motion links angular velocity with translational speed.


Angular Momentum about a Fixed Axis & Rolling Motion - VI


Description: Angular momentum depends on rotational inertia and angular velocity; rolling motion involves no slipping conditions.


Angular Momentum about a Fixed Axis & Rolling Motion - VII


Description: Angular momentum around a fixed axis: constant; rolling motion blends rotation and linear displacement.


Angular Momentum about a Fixed Axis & Rolling Motion - VIII


Description: Angular momentum conserves rotational motion; rolling motion requires rotational inertia and friction for no slipping.


Angular Momentum about a Fixed Axis & Rolling Motion -IX


Description: Angular momentum: product of inertia and angular velocity; rolling motion merges rotational and linear movements.


Synopsis of Gravitation - I


Description: Synopsis of Gravitation - I introduces the concept of gravitational force between two masses in space.


Synopsis of Gravitation - II


Description: Synopsis of Gravitation - II explores gravitational potential energy and the influence of gravity on objects.


Kepler's Laws - I


Description: Kepler's Laws - I covers the law of planetary orbits, stating planets move in elliptical paths.


Kepler's Laws II


Description: Kepler's Laws - II explains the law of equal areas, describing the speed of planetary motion.


Kepler's Laws - III


Description: Kepler's Laws - III discusses the law of harmonies, relating orbital periods to distances from the Sun.


Kepler's Laws - IV


Description: Kepler's Laws - IV elaborates on the mathematical derivations and applications of Kepler’s laws in astronomy.


Kepler's Laws - V


Description: Kepler's Laws - V focuses on advanced applications of Kepler's laws in satellite and planetary orbits.


Universal Law of Gravitation & Gravitational Constant - I


Description: Universal Law of Gravitation & Gravitational Constant - I introduces Newton's law of universal gravitation.


Universal Law of Gravitation & Gravitational Constant - II


Description: Universal Law of Gravitation & Gravitational Constant - II explores the gravitational constant and its role in calculations.


Universal Law of Gravitation & Gravitational Constant - III


Description: Universal Law of Gravitation & Gravitational Constant - III explains the relationship between gravitational force and mass.


Universal Law of Gravitation & Gravitational Constant - IV


Description: Universal Law of Gravitation & Gravitational Constant - IV discusses how gravity affects objects' motion on Earth.


Universal Law of Gravitation & Gravitational Constant - V


Description: Universal Law of Gravitation & Gravitational Constant - V covers calculations involving gravitational potential and kinetic energy.


Universal Law of Gravitation & Gravitational Constant - VI


Description: Universal Law of Gravitation & Gravitational Constant - VI explains gravitational fields and their impact on objects' acceleration.


Universal Law of Gravitation & Gravitational Constant - VII


Description: Universal Law of Gravitation & Gravitational Constant - VII discusses experimental validation of the law and gravitational constant.


Acceleration Due to Gravity of the Earth - I


Description: Acceleration Due to Gravity of the Earth - I introduces Earth's gravity and how it affects objects' free-fall acceleration.


Acceleration Due to Gravity of the Earth - II


Description: Acceleration Due to Gravity of the Earth - I explains Earth's gravitational pull and its effect on falling objects.


Acceleration Due to Gravity of the Earth - III


Description: Acceleration Due to Gravity of the Earth - II discusses variations in gravity based on altitude and Earth's shape.


Gravitational Potential Energy - I


Description: Gravitational Potential Energy - I introduces potential energy stored due to an object's position in a gravitational field.


Gravitational Potential Energy - II


Description: Gravitational Potential Energy - II covers the formula for calculating gravitational potential energy between two masses.


Gravitational Potential Energy - III


Description: Gravitational Potential Energy - III explains how gravitational potential energy changes with distance and mass.


Gravitational Potential Energy - IV


Description: Gravitational Potential Energy - IV explores applications of gravitational potential energy in planetary motion and orbits.


Acceleration due to Gravity Below and Above the Surface of Earth


Description: Acceleration due to Gravity Below and Above the Surface of Earth explains how gravity changes with altitude and depth.


Escape Speed - I


Description: Escape Speed - I introduces the minimum velocity needed for an object to escape Earth's gravitational pull.


Escape Speed - II


Description: Escape Speed - II covers the mathematical derivation and factors affecting escape speed, like mass and radius.


Escape Speed - III


Description: Escape Speed - III discusses practical examples and applications of escape velocity in space travel.


Earth Satellites - I


Description: Earth Satellites - I introduces artificial satellites and their orbits around Earth for communication, research, and navigation.


Earth Satellites - II


Description: Earth Satellites - II explains satellite types, including geostationary and low-Earth orbits, and their respective functions.


Earth Satellites - III


Description: Earth Satellites - III explores satellite launches, orbital paths, and how satellites stay in motion.


Earth Satellites -IV


Description: Earth Satellites - IV covers advanced applications of Earth satellites in weather monitoring, mapping, and space exploration.


Energy of an Orbiting Satellite - I


Description: Energy of an Orbiting Satellite - I explains the kinetic and potential energy of satellites in stable orbits.


Energy of an Orbiting Satellite - II


Description: Energy of an Orbiting Satellite - II discusses the conservation of mechanical energy for orbiting satellites.


Energy of an Orbiting Satellite - III


Description: Energy of an Orbiting Satellite - III explores energy transfers during satellite orbit changes or deorbiting.


Geostationary and Polar Satellites - I


Description: Geostationary and Polar Satellites - I introduces the difference between geostationary and polar orbits and their applications.


Geostationary and Polar Satellites - II


Description: Geostationary and Polar Satellites - II discusses the advantages of each orbit type in communication and Earth observation.


Weightlessness & Miscellaneous Questions - I


Description: Weightlessness & Miscellaneous Questions - I explains the concept of weightlessness experienced by astronauts in orbit.


Gravitational Potential - I


Description: "Gravitational Potential - I" explains the concept of gravitational potential energy and its calculation in gravitational fields.


Gravitational Potential - II


Description: "Gravitational Potential - II" explores gravitational potential due to spherical mass distributions and its impact on nearby objects.


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