Question

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 44 m/s. Assuming the baseball to be a uniform solid sphere, determine the rotational and translational kinetic energies of the ball in joules. KErotational = .197 Incorrect: Your answer is incorrect. What is the moment of inertia of a solid sphere? J KEtranslational = 145.2 Correct: Your answer is correct. J

Answer 1

1) Rotational kinetic energy: 0.098 J

2) Translational kinetic energy: 145.2 J

Explanation:

1)

The rotational kinetic energy of a rigid body is given by

$E_r =\frac{1}{2}I\omega^2$

where

I is the moment of inertia of the body

$\omega$ is its angular speed

The ball in this problem is a uniform sphere, so its moment of inertia about its axis is

$I=\frac{2}{5}mr^2$

where

m = 0.15 kg is the mass of the ball

r = 3.7 cm = 0.037 m is the radius

Substituting,

$I=\frac{2}{5}(0.15)(0.037)^2=8.2\cdot 10^{-5} kg m^2$

The angular speed of the ball is

$\omega=49 rad/s$

So, the rotational kinetic energy is

$E_r = \frac{1}{2}(8.2\cdot 10^{-5})(49)^2=0.098 J$

2)

The translational kinetic energy of the ball is given by

$E_k = \frac{1}{2}mv^2$

where

m is the mass

v is the linear speed

For the ball in this problem we have:

m = 0.15 kg

v = 44 m/s

Substituting, we find

$E_k = \frac{1}{2}(0.15)(44)^2=145.2 J$

Learn more about kinetic energy:

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