Impulse and Momentum: What's the Difference?

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Impulse and momentum are distinct quantities in physics, with impulse defined as the change in momentum of an object. Momentum is a measure of an object's motion, while impulse refers to the force applied over a period of time that results in that change. The discussion draws an analogy to banking, where individual transactions and overall account balance are treated as separate entities. Understanding the difference between these concepts is crucial for applying them correctly in various contexts. The distinction highlights the importance of recognizing how forces and time interact to affect motion.
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Why are impulse and momentum treated as different quantites?
 
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Gurasees said:
Why are impulse and momentum treated as different quantites?

Impulse is a change in momentum.

Why is a banking transaction and your account balance treated as different quantities?
 
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PeroK said:
Impulse is a change in momentum.

Why is a banking transaction and your account balance treated as different quantities?
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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