Four objects—a hoop, a solid cylinder, a solid sphere, and a thin, spherical s

Question

Four objects—a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell—each has a mass of 5.28 kg and a radius of 0.247 m.

(a) Find the moment of inertia for each object as it rotates about the axes shown in the table above. hoop kg · m2 solid cylinder kg · m2 solid sphere kg · m2 thin, spherical shell kg · m2 (b) Suppose each object is rolled down a ramp. Rank the translational speed of each object from highest to lowest. solid cylinder > thin spherical > solid sphere > hoop solid sphere > solid cylinder > thin spherical > hoop hoop > solid cylinder > solid sphere > thin spherical thin spherical > solid sphere > solid cylinder > hoop (c) Rank the objects' rotational kinetic energies from highest to lowest as the objects roll down the ramp. solid cylinder > thin spherical > solid sphere > hoop hoop > thin spherical > solid cylinder > solid sphere hoop > solid cylinder > solid sphere > thin spherical thin spherical > solid sphere > solid cylinder > hoop

Explanation / Answer

Part A)

Hoop = (5.28)(.247)^2 = .322 kg m^2

Solid cylinder = (.5)(5.28)(.247)^2 = .161 kg m^2

Solid Sphere = (2/5)(5.38)(.247)^2 = .129 kgm^2

Spherical Shell = (2/3)(5.38)(.247)^2 = .215 kg m^2

Part B)

Translational Speed is as follows

mhg = .5mv^2 + .5Iw^2 where I = some value (x) of mr^2 and w = v^2/r. The x is the coeffieicent of the object, .5, 1, (2/5) or (2/3)

This .5Iw^2 = .5(x)(mv^2)

gh = .5v^2 + (.5)(x)(v^2)

v = sqrt1/(.5 + .5x)(gh)

Thus the bigger number x, the smaller the velocity

Thus the highest is the solid sphere, then the solid cylinder, then the spherical shell, then the hoop

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