Energy conservation refers to the principle that energy cannot be created or destroyed, but only transformed from one form to another. This means that the total amount of energy in a closed system remains constant.
Centripetal acceleration is the acceleration towards the center of a circular path. It is always perpendicular to the velocity of an object and is caused by a centripetal force, such as tension in a string or the force of gravity.
According to the law of conservation of energy, the total energy of a system must remain constant. In the case of centripetal acceleration, the kinetic energy of an object is constantly changing as it moves in a circular path, but the total energy (kinetic + potential) remains the same.
Since energy cannot be created or destroyed, the total energy of a system must be conserved. This means that the energy used to maintain centripetal acceleration must come from somewhere, such as the potential energy of an object at a higher point on a circular path.
One example is a roller coaster. As the coaster moves up and down the hills, the energy is constantly being transformed between potential and kinetic energy, but the total energy of the system remains constant. Another example is a satellite orbiting the Earth, where the centripetal force of gravity keeps it in a circular path while energy is conserved.