A wheel is moving (no slipping) between two tracks. The radius of the inner circ

Question

A wheel is moving (no slipping) between two tracks. The radius of the inner circle is r1 and that of the outer circle is r2. The upper track is moving to the left and the lower track is moving to the right with velocities of v1 and v2, respectively. Both of the tracks are accelerating with accelerations a1 and a2, respectively. Find the acceleration of point P.

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Explanation / Answer

Angular rotation of small and big circles will be equal.

So, angular vel w = v1 / r1 = v2 / r2

and angular acceleration, alpha = a1 / r1 = a2 / r2

Acceleration of P = sqrt [(r1*w^2)^2 + (r1*alpha)^2]

a = r1*sqrt (w^4 + alpha^2)

a = r1* sqrt [ (v1 / r1)^4 + (a1 / r1)^2]

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