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

Question

Four objects—a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell—each has a mass of 4.05 kg and a radius of 0.225 m.

(a) Find the moment of inertia for each object as it rotates about the axes shown in the table above.

kg · m2

(b) Suppose each object is rolled down a ramp. Rank the translational speed of each object from highest to lowest.

(c) Rank the objects' rotational kinetic energies from highest to lowest as the objects roll down the ramp.

hoop     kg · m2 solid cylinder     kg · m2 solid sphere     kg · m2 thin, spherical shell    

kg · m2

Four objects-a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell-each has a mass of 4.05 kg and a radius of 0.225 m. (a) Find the moment of inertia for each object as it rotates about the axes shown in the table above. hoop kg m^2 solid cylinder kg m^2 solid sphere kg m^2 thin, spherical shell kg m^2 (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

(a) moment of inertia of hoop = 4.05*0.2252 = 0.205 kg · m2 solid cylinder = 0.205/2 = 0.1025 kg · m2 solid sphere = (2/5)*0.205 = 0.082 kg · m2 thin sperical shell = (2/3)*0.205 = 0.1367 kg · m2 (b) we have accelaration inversely proportional to moment of inertia so the velocity will also be inversely proportional to moment of inertia so the answer is : solid sphere > solid cylinder > thin spherical > hoop (c) we have rotaional kinetic increases with increase in moment of inertia so the answer is : hoop > thin spherical > solid cylinder > solid sphere

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