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 4.44 kg and a radius of 0.245 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.
5. 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.
6. 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

given that mass = m = 4.44kg   and radius R = 0.245m a) the moment of inertia
hoop: I= MR² = 4.44 kg* (0.245 m)^2 = 0.266kg·m²
solid cylinder: I= (1/2)MR² = 0.133 kg·m²
solid sphere: I= (2/5)MR² = 0.106 kg·m²
thin, spherical shell: I= (2/3)MR² = 0.177kg·m²

(b)
solid sphere > solid cylinder > thin spherical > hoop
translational speed is inversely proportional to the moment ofinertia .so if moment of inertia is least its translational speedis more

(c)
hoop > thin spherical > solid cylinder > solid sphere ROTATIONAL KINETICENRGY IS DIRECTLY PROPORTIONAL TO MOMENT OF INERTIA

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