A hoop of mass M and radius R rest horizontally on a smooth table (like in probl

Question

A hoop of mass M and radius R rest horizontally on a smooth table (like in problem 7-35 in Classical Mechanics by John R. Taylor). However, this time, one point on the circumference is now pinned to the table so that the hoop may swing freely in the horizontal plane about that pinned point and a cute little bug of mass m crawls at constant speed vo about the circumference of the hoop.

a) First, set up the equations of motion for this problem by choosing to view it as a two coordinate problem (i.e. two degrees of freedom) with the force that the bug exerts against the hoop to be determined from the condition that the bug moves with constant speed along the rim of the hoop.

b) Second, set up the equations of motion for this problem by choosing to view it as one coordinate problem (i.e. only one degree of freedom) and with a time dependent constraint embedded in the geometry of the problem at the outset. Show that the two formulations yield equivalent equations of motion for the hoop.

Explanation / Answer

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