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Wheel in a cylinder problem

by ranger1716
Tags: cylinder, wheel
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Oct13-05, 07:07 PM
P: 18
wondering if someone could shed some light on this problem.

a wheel of radius r rolls around the interior of a cylinder of radius R. assume that the center of the cylinder is at the origin and at time t=0, the point of tangency is at the point (R,0). let P denote the original point of tangency on the wheel. we will investigate the motion of this point P on hte wheel. let vector v sub 1 (t) denote the vector emanating from the center of the wheel and ket theta(t) denote the angle v sub 1 (t) makes with the x-axis at time t. let vector v sub 2 (t) be the vector that emanates at the center of the wheel and terminates at P and let phi(t) be the angle that vector v sub2(t) makes with the horizontal at time t.

show that phi(t)=((R-r)/r)(theta(t))

I'm having trouble beginning this proof.

Any help would be appreciated.
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