Conservation Laws

Fundamental Concepts

Conservation of energy: The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. This means that the total amount of energy in a closed system remains constant. Energy can be transferred from one object to another, or it can be transformed from one form to another (e.g., potential energy to kinetic energy), but the total amount of energy remains the same.Conservation of mass: The law of conservation of mass states that the mass of a closed system remains constant over time. This means that matter cannot be created or destroyed, only transformed from one form to another. For example, during a chemical reaction, the total mass of the reactants is equal to the total mass of the products.Conservation of momentum: The law of conservation of momentum states that the total momentum of a closed system remains constant over time. Momentum is defined as the product of an object's mass and velocity. This means that in a closed system, the total momentum of all objects remains the same, regardless of any internal forces or collisions between the objects.Impulse-momentum theorem: The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it. Impulse is the product of the force applied to an object and the time it acts, and it is equal to the change in momentum of the object. Mathematically, FΔt = Δp, where F is the force applied to the object, Δt is the time over which the force acts, and Δp is the change in momentum of the object.

Conservation Law Equations


Conservation of energy: The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. The equation for conservation of energy is E_final = E_initial, where E_final is the final energy of a system, and E_initial is the initial energy of the same system.
Conservation of momentum: The law of conservation of momentum states that the total momentum of a closed system remains constant, unless acted upon by an external force. The equation for conservation of momentum is P_final = P_initial, where P_final is the final momentum of the system, and P_initial is the initial momentum of the same system.
Conservation of angular momentum: The law of conservation of angular momentum states that the total angular momentum of a closed system remains constant, unless acted upon by an external torque. The equation for conservation of angular momentum is L_final = L_initial, where L_final is the final angular momentum of the system, and L_initial is the initial angular momentum of the same system.
Conservation of mass: The law of conservation of mass states that mass cannot be created or destroyed, only transformed from one form to another. The equation for conservation of mass is M_final = M_initial, where M_final is the final mass of the system, and M_initial is the initial mass of the same system.