# How can the linear momentum can be understood physically?

Currently reading Classical Mechanics by Herbert Goldstein, and I'm trying to understand every concept physically. Speed can be understood physically, as the distance traveled within a certain amount of time, it makes sense to me. By contrast, I can't attribute a physical explication to linear momentum. How can I understand it physically? Why do we multiply mass by speed?

## 3 Answers

Speed can be understood physically, as the distance traveled within a certain amount of time, it makes sense to me. By contrast, I can't attribute a physical explication to linear momentum. How can I understand it physically? Why do we multiply mass by speed?

'speed' (or velocity) is the measure of 'motion' and is related to KE, a unitary mass acquires 'speed' equal to the square root of twice its KE, as you know, if v = 10, in one second the body travels the distance of 10 metres

By 'mass' whe mean the total mass of a body, the sum of all unitary masses . The relation of mass and speed is like the relation between sweets and jars: if 1 jar contains 10 sweets each, 2 jars contain 20 sweets (2 is the total mass of the jars).

Why whould more matter in movement would imply more motion? – Chirac

2 jars * 10 sweets is 20 = the 'quantity of sweets'. Has a jar anything to do with sweets? jars by sweets = total quantity of sweets, p = m * v, masses by velocity is the total 'quantity of motion'. Momentum is the quantity of motion that a body possesses p = m * v, and depends on the value of speed and the number of unitary masses of a body. The greater its momentum, the greater the force it takes to stop it, the greater the force of impact on another body.

The idea of momentum is the idea of "quantity of motion". You want to be able to formulate in some sense the idea of "how much motion there's in this particle?" and you can think about the simplest model for that like that: the faster the particle moves intuitively more motion there is, so the quantity of motion should be proportional to the velocity. Also, if we agree that mass is a measure of quantity of matter, the more mass there is, more matter in movement you have and so more motion. In that case, quantity of motion should be proportional to mass as well. In that case, you can simply choose units such that this becomes equality, so that you define $\mathbf{p} = m\mathbf{v}$.

You cannot understand this notion without considering the equations of motion. The force $\mathbf{F}$ during interval $dt$ changes a quantity $m\mathbf{v}$ by an addendum $\mathbf{F}dt$: $$d(m\mathbf{v})=\mathbf{F}dt$$ That's it.