A baseball has a mass of 0.15 kg and radius 3.7 cm. In a baseball game, a pitcher throws the ball with a substantial spin so that it moves with an angular speed of 49 rad/s and a linear speed of 52 m/s. Assuming the baseball to be a uniform solid sphere, determine the rotational and translational kinetic energies of the ball in joules. KErotational = Incorrect: Your answer is incorrect. What is the moment of inertia of a solid sphere? J KEtranslational = J Additional Materials

KE Rotational = 0.0986 J

KE Translational = 202.8 J

Explanation:

The rotational kinetic energy is given by:

KE Rotational = (1/2)Iω²

Where;

I = moment of inertia of a uniform solid sphere = (2/5)mr²

m = mass of sphere = 0.15 kg

r = radius of sphere = 0.037 m

ω = angular velocity (spin rate) = 49 rads/sec

Thus, KE Rotational = (1/2)(2/5)(0.15 x 0.037²)(49²) = 0.0986 J

The translational kinetic energy is:

KE Translational = (1/2)mv²

m = ball's mass = 0.15 kg

v = ball's velocity = 52 m/s

KE Translational = (1/2)(0.15)(52²) = 202.8 J

the temperature in kelvin of 2.0 dm3 of an ideal gas is doubled and its pressure is increased by a factor of four. what is the final volume of the gas