Time derivative Definition and 63 Threads

Did I understand correctly that relativistic momentum is p(t) = m\cdot\gamma(t)\cdot v(t), where \gamma = c/\sqrt{c^2-v^2} and c is the speed of light? For the fun of it I wrote down the time derivative and got {d\over dt}p(t) = \gamma^3(t)\cdot a(t) with a(t) = d v(t)/dt. Yet I...

Homework Statement Im am attempting to solve very difficult kinematics for a problem in my Dynamics course, and after what I got for the velocity of the particle, I come accros the problem that i can't diferentiate one part. Essentially I have to get the time derivative of...

Homework Statement Show that the time derivative of the potential energy can be written as dv/dt=-F1xV1x + (-F2xV2x) Homework Equations just proving it The Attempt at a Solution i haven't learned partial derivatives yet...so kind of confused. V=0.5mv^2...V'=mv...clearly not what...

Okay, so I'm at a loss for words to describe my irritation and curiosity on how this is solved. Given the one-dimensional wave equation (i.e. u_tt=c^2*u_xx 0<x<L, t>0) with no source and constant velocity, we define the energy associated with the wave to be E=integral from 0 to L of...

Hi i was just wondering why do we stop with only the second order derivative of displacement which is the acceleration. I was wondering if there is no scenario in the world where we would need the third order time derivative which might talk about how the acceleration varies with respect to...

How does one take the time derivative of ϒmv ? I tried treating gamma and mv as separate functions but it just gets messy and ultimately wrong.

In the solution of a pendulum attached to a wheel problem, I was initially suprised to see that a term of the form: \frac{df}{dt} "can be removed from the Lagrangian since it will have no effect on the equations of motion". ie: L' = L \pm df/dt gives identical results. f in this...

So I had a QM test today and I needed to show that the energy operator is hermitian. This was easy to show provided that the the adjoint of d/dt is -d/dt. I know this is the case for the spatial derivative but is it the case with the time derivative? The bra-ket is an integral over x not time...

Could someone please help with this question. For non-inertial frames show that the in-frame time derivative D obeys: D(fa)=fDa+df/dta Where f is a scalar function and a is a vector. I know that Df=df/dt and that Da= the sum of the derivatives of the components of a times the relavant...

Hi all, got a little caught up in tonights homework assignment; which basically reads: Find an expression for \frac {d<\hat{p}>} {dt} in terms of V(x). I had a few ideas from my math methods for theoretical phys. class i took a few quarters ago, involving applying the derivative operator...

1-How could an RL combination be connected to produce an output voltage which is the time derivative of the input voltage? 2-Show that taking the time derivative of a sinusoidal function [such as cos(wt+a)] always has the effecton increasing its phase pi/2. 3-İf the internal series...

Which is more generally corrrect, F=ma or F=dp/dt ?

Hi, Physics books gloss over math. Sometimes it bothers me. Given a separable function of time and position f = h(x)g(t) then d / dt of [inte] h(x)g(t)dx = [inte] h(x) dg(t)/dt dx Where the derivative in the second integral is a partial deriv. Why the chain rule does not apply...