Recent content by LioNiNoiL

That should be (of course) d(KE)/dx = (1/v)d(KE)/dt Mistakes happen after a long day.

From the diagram, the pertinent measurements are L and R2 (which are fixed) and y which varies as the step motor is turned. The angle of interest (call it θ) is the angle opposite side L of the triangle formed by lengths L, R2, and y. By the Law of Sines, the ratio L/sinθ = D (the diameter...

equivalence No, it means they are equivalent ("equal worth") in some well-defined way. In your example F=ma , the left side (F) is not the same as the right side (ma) but the numerical quantities will be equivalent, and the dimensional unit of F (Newton) will be equivalent to the dimensional...

KE(t) I get the same result as HallsofIvy, by a different route: KE = ½mv² , so d(KE)/dt = mv(dv/dt) = (ma)v = Fv therefore F = (1/v)d(KE)/dt ... (eq'n A) and d(KE)/dx = mv(dv/dx) = mv(dv/dt)(dt/dx) = m(dv/dt) = ma = F , because dt/dx is the reciprocal of v so d(KE)/dt =...

For this result, you must restrict the sequences {pi} to those for which ##\sum_{i=1}^\infty p_i## converge, because the inclusion of sequences for which the sum does not converge will clearly prevent the existence of an expected value (mean) of your distribution. There may also be restrictions...

Chris Caldwell lists the Wilans function for ##p_n## at the bottom of the page at: http://primes.utm.edu/notes/faq/p_n.html