# Linear momentum

#### Prerequisite

When we formulated our description of motion we began with kinematics — specifying where an object is as a function of time. Newton's second law arose from our choices about how to describe motion — by focusing on individual objects and their interactions with other objects and through our observations about how objects behaved when subject to interactions (forces). This led to see lots of things — such as invisible forces — and to reorganize our observations and experiences of the everyday world.

But there is still something unsatisfying about it. People who haven't studied Newtonian theory often have the sense that when an object experiences a force that makes it move, that force "gives something to the object" that the object then carries with it that keeps it moving. Think about a strongly thrown ball or a high-speed train. These objects are hard to stop! They seem to carry something in their motion that is related to a force — the force that is needed to stop them. Of course this contradicts the everyday sense that "motion dies away naturally" — an everyday sense we have that arises, as we now know from our Newtonian analysis, from forgetting about the "invisible" force of friction. The Newtonian theoretical framework nicely resolves this apparent contradiction by helping us to be more explicit about the actors involved in changing motion.

Can we find "what a moving object carries that makes it hard to stop" within our Newtonian system? The answer is yes. We call it ** linear momentum**. As a consequence of Newton's 3rd law, it has some remarkable properties — ones that allow us to figure out things about interacting objects even when we don't know anything about the force. This result will be of considerable importance as we begin to work out the connection between the properties of atoms and molecules and the properties of matter that we observe directly at a personal level. These are explained in the follow-on readings.

Joe Redish 10/18/11

#### Follow-ons

Last Modified: February 8, 2019