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# The center of mass of a pitched baseball or radius 3.34 cm moves at 25.4 m/s?

. The ball

spins about an axis through its center of mass

with an angular speed of 194 rad/s.

Calculate the ratio of the rotational energy

to the translational kinetic energy. Treat the

ball as a uniform sphere.

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- WhomeLv 71 month agoFavorite Answer
KEr/KEt = ½Iω² / ½mv² = Iω² / mv² = (2mR²/5)ω² / mv² = 2R²ω² / 5v²

KEr/KEt = 2(0.0334²)(194²) / 5(25.4²) = 0.0260

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- oubaasLv 71 month ago
KEr = J/2*ω^2 = 1/5 m*r^2*ω^2 = m*3.34^2*10^-4*1.94^2*10^4/5 = 8.4 m

Ket = m/2*V^2 = 25.4^2/2*m = 322.6*m

KE = KEr+KEt = 331*m

KEr/KEt = 8.4/322.6 = 0.0260

KEr/KE = 8.4/331 = 0.0254

KEt/KE = 322.6/331 = 0.975

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