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Classical Mechanics
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Classical mechanics is the branch of physics that deals with the motion of macroscopic objects, their causes, and their effects.
The fundamental concepts in classical mechanics include space, time, mass, force, momentum, energy, and the laws of motion.
Newton's first law, also known as the law of inertia, states that an object at rest remains at rest, and an object in motion remains in motion with constant velocity, unless acted upon by an external force.
Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Force = mass × acceleration.
Newton's third law states that for every action, there is an equal and opposite reaction. Forces always come in pairs, and the two forces are equal in magnitude and opposite in direction.
Scalar quantities have magnitude only, while vector quantities have both magnitude and direction.
Displacement is the change in position of an object, distance is the total length of the path traveled, and velocity is the rate of change of displacement with respect to time.
Acceleration is the rate of change of velocity with respect to time.
Mass is the measure of the amount of matter in an object, while weight is the force exerted on an object due to gravity.
The principle of conservation of momentum states that in a closed system, the total momentum remains constant unless an external force acts on the system.
The principle of conservation of energy states that energy cannot be created or destroyed, but it can be transformed from one form to another.
Potential energy is the energy an object possesses due to its position or state, while kinetic energy is the energy an object possesses due to its motion.
In an elastic collision, kinetic energy is conserved, while in an inelastic collision, kinetic energy is not conserved, and some energy is dissipated as heat or sound.
Translational motion is the motion of an object along a straight or curved path, while rotational motion is the motion of an object around a fixed axis.
Static friction is the force that prevents an object from starting to move, while kinetic friction is the force that opposes the motion of an object after it has started moving.
Centrifugal force is an apparent force that acts outward on a rotating object, while centripetal force is the force that makes an object follow a curved path.
Uniform motion is motion with constant velocity, while non-uniform motion is motion with varying velocity.
Linear momentum is the product of mass and linear velocity, while angular momentum is the product of moment of inertia and angular velocity.
Conservative forces are forces for which the work done in moving an object between two points is independent of the path taken, while non-conservative forces are forces for which the work done depends on the path taken.
An open system can exchange energy and matter with its surroundings, while a closed system can exchange energy but not matter with its surroundings.
In an equilibrium system, the net force and torque acting on the system are zero, while in a non-equilibrium system, there are non-zero net forces or torques acting on the system.
Static equilibrium is a state of balance with no motion, while dynamic equilibrium is a state of balance with constant motion.
Work is the product of force and displacement, while power is the rate at which work is done or energy is transferred.
Impulse is the product of force and time, while momentum is the product of mass and velocity.
Torque is the measure of the tendency of a force to cause rotational motion, while angular momentum is the measure of the amount of rotation an object has.
Simple harmonic motion is a type of periodic motion where the restoring force is proportional to the displacement, while periodic motion is any motion that repeats itself over time.
Stress is the force per unit area applied to an object, while strain is the deformation or change in shape or size of an object due to the applied stress.
Rigid bodies maintain their shape and size when external forces are applied, while deformable bodies change their shape and size when external forces are applied.
Elastic deformation is a temporary change in shape or size that is recovered when the external force is removed, while plastic deformation is a permanent change in shape or size that is not recovered when the external force is removed.
Free-body diagrams show all the forces acting on an object, while kinetic diagrams show the motion of an object and the forces causing that motion.
In longitudinal waves, the particles of the medium vibrate parallel to the direction of wave propagation, while in transverse waves, the particles of the medium vibrate perpendicular to the direction of wave propagation.
Reflection is the change in direction of a wave at the boundary between two different media, while refraction is the change in speed and direction of a wave as it passes from one medium to another.
Interference is the superposition of two or more waves, while diffraction is the bending of waves around obstacles or through apertures.
Standing waves are waves that do not propagate, while traveling waves are waves that propagate through a medium.
Damped oscillations are oscillations that decrease in amplitude over time due to energy dissipation, while forced oscillations are oscillations that are driven by an external periodic force.
Resonance is the condition where a system is driven at its natural frequency, resulting in large-amplitude oscillations, while beat frequency is the difference between two close frequencies, resulting in a periodic variation in amplitude.
Linear kinematics deals with the motion of objects along a straight line, while rotational kinematics deals with the motion of objects around a fixed axis.
Linear dynamics deals with the forces and motion of objects along a straight line, while rotational dynamics deals with the torques and rotational motion of objects about a fixed axis.
Particle dynamics deals with the motion of a single particle or point mass, while rigid body dynamics deals with the motion of an extended body that maintains its shape and size.
Statics deals with the study of forces and torques on objects that are at rest or in equilibrium, while dynamics deals with the study of forces and torques on objects that are in motion.
Lagrangian mechanics is a formulation of classical mechanics based on the principle of least action and generalized coordinates, while Hamiltonian mechanics is a formulation based on the energy and momentum of the system.
Holonomic constraints are constraints that depend only on the positions of the system, while non-holonomic constraints depend on both the positions and velocities of the system.
Conservative systems are systems where the total energy is conserved, while non-conservative systems are systems where the total energy is not conserved due to the presence of non-conservative forces.
Deterministic systems are systems where the future state can be predicted precisely from the initial conditions, while stochastic systems are systems that involve randomness or uncertainty.
Classical mechanics describes the motion of macroscopic objects, while quantum mechanics describes the behavior of particles at the atomic and subatomic scales.