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...