Recent content by Trapezoid

Thanks to everyone for your quick replies and kudoes to genericusrname - that explanation really helped. I still, however, have a bit of trouble seeing how it relates to surface integrals. An infinitesimally small portion of the surface of a solid is represented by ds = \sqrt{dx^2 + dy^2 +...

Homework Statement My question is not specific to any particular problem but is rather of a conceptual nature. In my advanced calculus class this semester, the notation ds appears often, for line integrals, surface integrals, and arc length. In all honestly, I don't really understand what ds...

Thanks tiny-tim, Let me make sure that I understand correctly. Is \frac{r}{|r|} the unit vector for motion in the radial direction?

Hi tiny-tim, It is my understanding that the tangential and circumferential components are different. When I say the circumferential component of acceleration, I refer to the acceleration in the direction of \theta, ie: the change in the rate of change of \theta. I'm having trouble finding...

Homework Statement Let \vec{R} = (t + \sin t) \hat{i} + (t + \cos t) \hat{j} denotes at time t the position of a moving particle. Determine the radial and circumferential components of acceleration as a function of t. Homework Equations v_r = \dot{r} v_{\theta} = r\dot{\theta}...

Hi all, Sorry to bump but we got the solutions to the assignment so I thought I'd post some more guidance in case anybody else is having trouble with a similar question. The method outlined by HallsofIvy is correct. Without giving too much away, to solve the last integral, substitute u =...

Thanks HallsofIvy and RoshanBBQ, Unless I've misunderstood, the method outlined by HallsofIvy leaves me with the integral \int \frac{dx}{\sqrt{\ln(\frac{x}{L})}} which I cannot even begin to solve. With regards to RoshanBBQ's solution, it seems odd to me that k would be negative since...

Thanks for all the help everybody. I'll take a closer look to see if I can't find the answer from here.

This question is from my calculus assignment but I apologize if it belongs on the a physics board regardless. Homework Statement A particle of mass m is attracted towards a fixed point 0 with a force inversely proportional to its instantaneous distance from 0. If a particle is released...