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    Physics: Sphere and Cylinder having different accelerations down a plane.

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    See attachment #1 for diagram showing parameters

    At the upper end of an inclined plane of length L, a uniform sphere is released from rest. At the same instant, a uniform cylinder is released from rest at distance d ahead of the sphere such that both sphere and cylinder arrive at the same time at the lower end of the plane.

    a. The distance d is what fraction of length L?
    b. At the instant they both reach the lower end of the plane, find the ratio of their linear velocities Vcyl/Vsph.

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    Solution Preview

    part a.
    Let d be the fraction f of the total length L. In other words, (1) d= f L.
    Also let b = angle of the plane, A = angular acceleration, a= linear acceleration, (recalling that a = R A), and let t = the equal time of travel.
    Moments of inertia must be about this contact axis, found by translation theorem, 'Ip = Io + M ...

    Solution Summary

    The solution presents all the calculations to arrive at the answers. The spheres and cylinders having different accelerations down a plane are given.