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

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.


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.