For the following objects, which all roll without slip- ping, determine the rotational kinetic energy about the center of mass as a percentage of the total kinetic energy: (a) a solid sphere, (b) a thin spherical shell, and (c) a tiin cylindrical shell.

The answers to the question are

(a) 28.57 %

(b) 40 %

(c) 50 %

Explanation:

The following are the relations between total and rotational kinetic energies of a sphere

=

ω = angular velocity

v = velocity

m = mass

I = Moment of inertia =  and ω = v/r

Therefore =

Therefore

= 28.57 %

(b) for a thin sherical shell, I = Therefore

= = = 1/3mv²

KE(Total) = KE(Transitional) + KE(Rotational) = 1/2mv² + 1/3mv² = 5/6mv²

KE(Transitional) /KE(Total) = (1/3mv²)/(5/6mv²) = 6/15

Percentage total = 6*100/15 = 40 %

(c) Thin cylindrical shell = I = and

Therefore

and

In percentage = = 50 %

the moon affects the earth gravitation ally, causing certain motions of that body and also producing tides in its ocean and atmosphere. the tidal wave in our atmosphere is, however, far too minute to be an effective cause in any known meteorological phenomenon.

explanation:

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