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 50 rad/s and a linear speed of 48 m/s. Assuming the baseball to be a uniform solid sphere, determine the rotational and translational kinetic energies of the ball.

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aristeus aristeus · Answer 1 · 2019-11-05T07:41:54+01:00

Answer:

Rotational kinetic energy is 0.513 j

Transnational kinetic energy is 172.8 j

Explanation:

We have given mass of the baseball m = 0.15 kg

radius r = 3.7 cm = 0.037 m

Angular velocity is given as [tex]\omega =50rad/sec[/tex]

Linear velocity v = 48 m/sec

We know that moment of inertia is given by [tex]I=\frac{1}{2}mr^2=\frac{1}{2}\times 0.15\times 0.037^2=1.026\times 10^{-4}kgm^2[/tex]

Now rotational kinetic energy is given by

[tex]KE_{rotational}=\frac{1}{2}\times 1.026\times 10^{-4}\times 50^2=0.513j[/tex]

Now transnational kinetic energy is given by [tex]KE_{translational}=\frac{1}{2}mv^2=\frac{1}{2}\times 0.15\times 48^2=172.8j[/tex]