THE PROBLEM A pitcher has thrown the baseball toward the batter at v=115 km/h. T
ID: 1786934 • Letter: T
Question
THE PROBLEM A pitcher has thrown the baseball toward the batter at v=115 km/h. The ball is also spinning around its center at =6 revolutions per second. The radius of the ball is r-3.5 cm. What fraction of the ball's kinetic energy is rotational? PAPER SOLUTION INTERPRET Identify all of the true statements. A. We have all of the information we need to calculate a ratio of kinetic energies due to linear motion. due to rotational motion. B. We have all of the information we need to calculate the kinetic energy OC. We have all of the information we need to calculate the kinetic energy D. None of the above. DEVELOP Derive an algebraic expression for the fraction of kinetic energy. In your answer, type w to represent a. rotational Kion totalExplanation / Answer
K(rotational) = Iw2/2
where I is moment of inertia of ball and I = 2 mr2/5
K(rotational) = mr2w2/5
K(translational) = mv2/2
Hence K(rot)/ K(total) = 2 r2w2/(5v2+2r2w2)
w = 2 pi *6 = 12 pi rad /sec
v = 115 km /hr = 31.9 m/sec
r = 0.035 m
K(rot)/K(total) = 6.8x10-4
As we don't know mass, we can't find KE due to linear or rotational motion, but we can find ratio of the two, as mass term gets cancelled.
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