## Apostol, Vols 1 and 2

February 15th, 2008
If a moving particle has mass *m*, Newton’s second law of motion states that the force acting on it (due to its acceleration) is the vector *m a(t)*, mass times acceleration. If the particle moves on a circle with constant angular speed, this is called a centripetal force because it is directed toward the center. This force is exerted by the mechanism that confines the particle to a circular orbit. The mechanism is a

*string*in the case of a stone whirling in a slingshot, or

*gravitational attraction*in the case of a satellite around the earth. The equal and opposite reaction (due to Newton’s third law), that is, the force -

*m*, is said to be centrifugal, or “center-fleeing.”

**a**(t)It is easy to imagine then, in the park, that the confining mechanism of two children spinning circles around each other is the pair of pairs of clasped hands. It is less easy to imagine the wall of the elevator you leaned against, inhaling strangers, pushing you with equal and opposite force. Newton’s third law is then best illustrated by a girl on rollerskates, who you met in the hallway halfway to the coffee machine. She places both her palms on yours, and pushes, firmly. She rolls down the hall, backwards and away. You stand still. You are pushing back just as hard.