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Re: [Phys-l] real-world mechanics problem

That's the prob. cos(theta) ~ = 1-theta squared / 2 ** This is an ~ while the other method [total E = angular KE + PE = K = either at their appropriate extrema (turning points?)] involves no approximation.

Also for Bob S = L theta (small angle approx. chord = line segment) Then s dot = L theta dot.

** Soooo convenient. And rather accurate in the range of long period clock pendula. e.g. tower clock at Trinity College *** is ~ 50 mR. cos(50E-3) = 0.998750260 and 50E-3 ^ 2 / 2 = 0.998750000 a difference of 2.604 E-7 This difference is detectable over a short time (minutes?) by the MicroSet: ****

"MicroSet has a resolution of one microsecond and shows rates as Seconds Per Beat (to six decimal places) or as Beats Per Hour (to two decimal places). The timebase in MicroSet is trimmed to +/- one part per million."




*** http://mb.nawcc.org/showthread.php?t=68648

**** http://www.bmumford.com/mset/choosing.html

bc


On 2011, Feb 04, , at 00:39, Bob Sciamanda wrote:

?BC,
Agreed, .5mv^2 = mgh .

But how do you turn X dot =SQRT(2gL[1-CosA])
into
X dot = sqrt.(g*L) A ?

-Bo