The Reason Why Momentum is Denoted by p
Explanation
Many of the symbols used in physics can be easily understood why they were chosen without much thought. For example, the symbols for force, mass, velocity, and acceleration denoted by $\mathbf{F}$, $m$, $\mathbf{v}$, and $\mathbf{a}$ respectively, can be easily guessed to originate from the first letter of the corresponding English words force, mass, velocity, acceleration. However, the symbol for momentum is $\mathbf{p}$, even though momentum is the term used in English. One could understand the need for a different symbol since using $m$ would clash with the symbol for mass, but it might be hard to come up with ‘why $\mathbf{p}$?’. This curiosity might seem trivial, but until one hears a satisfactory answer, it incessantly occupies the mind, impeding focus on other tasks. Upon searching, I found two speculations. I find the first hypothesis more plausible.
Originated from impetus1
It is said that at the time when Newton published the Principia, the scientific community used the term ‘impetus’ for ’the property of moving objects’. ‘Pellere’ is the infinitive form of the Latin verb pello, meaning ’to push forward’, from which it seems words like impetus, push, pulse, pull are derived. Hence, the word impetus was used in the scientific community, and taking the core letter p, it seems logical that $\mathbf{p}$ was proposed as the symbol for momentum.
At that time, it was not momentum but pmentum2
Without the need for further explanation, at that time, the English word for momentum was not momentum but pmentum, hence by taking the first letter, $\mathbf{p}$ was chosen as the symbol.