Derivative of momentum...

[MDJH]

Momentum is a vector quantity, in the same direction as speed, and velocity is the magnitude and direction of said speed, with mass being the scalar coefficient by which velocity is multiplied to yield momentum, right? So let's say we're taking the derivative of momentum with respect to time (seeing as how that's what net force actually is) and mass of a particular object is transferring elsewhere... if we're analyzing the momentum of the object in particular, and both mass and velocity are changing at the same time, would the rate of change in momentum be:

 

(dp/dt) = (dm/dt)*(dv/dt)

 

OR

 

(dp/dt) = m*(dv/dt) + v*(dm/dt)

 

OR would it be something else because of the differing natures of the quantities involved?

[ajb]

Your second answer is correct, recall Leibniz's rule.

[MDJH]

Leibniz' rule? I'm not sure if I've heard of that one.

 

Though if you're referring to the product rule, then yeah that's what I assumed applied in the 2nd case. I just wasn't sure if it worked differently when you had the product of a scalar and vector or something...

[ajb]

Leibniz' rule? I'm not sure if I've heard of that one.

 

It is another name for the product rule.