There is a gravitational force of attraction between the Earth and the moon, but is it mutual? That is, are the forces on the Earth and the moon equal? Most people would say no, the Earth exerts a greater force of attraction because it is larger and has more mass. This is a situation in which Newton’s Third Law is relevant. Newton’s Third Law says that for every force, there is an equal and opposite reaction force. So the force the Earth exerts on the moon must be exactly equal and opposite the force the moon exerts on the Earth. But how can that be – that the same size force keeps the moon orbiting, but barely affects the Earth? The answer is inertia – the tendency for all objects with mass to maintain their state of motion. Since the Earth has much more mass than the moon, it has greater inertia and therefore experiences much less acceleration for the same amount of force.
A review of linear algebra as necessary for quantum mechanics, including vector properties, inner products, normalization, and representations of vectors in a basis. (This lecture is part of a series for a course based on Griffiths’ Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/playlist?list=PL65jGfVh1ilueHVVsuCxNXoxrLI3OZAPI.)