Putting a simple momentum equation into words

by tolove
Tags: equation, momentum, putting, simple, words
 P: 161 Check the accuracy of my wording for these first two equations, then, if you could, try to explain the last equation for me. Ʃ F = dp/dt "The total net force acting on a particle is equal to the rate of change of momentum over time." ∫ Ʃ F dt = ∫ dp/dt dt "The sum of the total net force acting on a particle over a time interval is equal to the sum of the rate of change of momentum over a time interval." My physics book breaks up differentials like this very regularly so as to make it clear for integration. But my question is, is this step a meaningful equation, or is this simply mathematical notation? Ʃ F dt = dp Thanks!
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P: 26,148
hi tolove!
 Quote by tolove Ʃ F = dp/dt "The total net force acting on a particle is equal to the rate of change of momentum over time."
yes, except …

"total" and "net" mean the same, so you needn't use both

personally, i'd say that "rate" means "over time", so i'd leave that out also
 ∫ Ʃ F dt = ∫ dp/dt dt "The sum of the total net force acting on a particle over a time interval is equal to the sum of the rate of change of momentum over a time interval."
"sum" is definitely wrong

it's an integral (and there's no simple-english alternative to that word)

and you need to use the word "same" … "over the same time interval"
 My physics book breaks up differentials like this very regularly so as to make it clear for integration. But my question is, is this step a meaningful equation, or is this simply mathematical notation? Ʃ F dt = dp
it's mathematically meaningful (it's a statement about mathematical objects called "differentials"),

but it has no physical meaning, except as a limit or an approximation: it would never apply to an actual time interval (unless everything is constant)
P: 161
 Quote by tiny-tim hi tolove!
To correct the first one,
Ʃ F = dp/dt
"The net force acting on a particle is equal to the change of momentum over time."

and for ∫ Ʃ F dt = ∫ dp/dt dt,

"The integral of the total force acting on a particle over a certain time interval is equal to the integral of the rate of change of momentum over the same time interval."

And if I wanted to remove the word "integral," I could put the Reimann sum notation into words.

These don't make good bedtime stories. Thank you for clearing up that third equation for me! That has been driving me nuts.

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Thanks
P: 26,148
Putting a simple momentum equation into words

hi tolove!
 Quote by tolove "The net force acting on a particle is equal to the change of momentum over time."
oops!

i should have been clearer … i meant leave out "over time" … you do need the words "rate of"!
 "The integral of the total force acting on a particle over a certain time interval is equal to the integral of the rate of change of momentum over the same time interval."
the integral of a rate of change is just the original function, so you could shorten that to:

"The integral of the total force acting on a particle over a certain time interval is equal to the change of momentum over the same time interval."

(and of course you can shorten "The integral of the total force" to "The impulse" )
 And if I wanted to remove the word "integral," I could put the Reimann sum notation into words.
how?

(without taking several paragraphs and making it really confusing )
P: 161
 Quote by tiny-tim how? (without taking several paragraphs and making it really confusing )
Yep! By making it long and confusing.

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