Physics: The center of mass of a pitched baseball or radius 2.42 cm moves at 23.3 m/s. The ball spins about an axis through its center of mass with an angular speed of 158 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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The center of mass of a pitched baseball or radius

Ответ:

marchellamazz123

23.01.2022

To solve the problem, it will be necessary to define the rotational and translational kinetic energy in order to determine the relationship between the two. Rotational energy is defined as,

$KE_{Rotational} = \frac{1}{2} I\omega^2$

Here,

I = Moment of Inertia

$\omega$ = Angular velocity

Now the translational energy will be,

$KE_{Translational} = \frac{1}{2} mv^2$

Here,

m = Mass

v = Velocity

Therefore the relation between them will be,

$\frac{KE_{Rotational} }{KE_{Translational}} = \frac{\frac{1}{2} I\omega^2 }{\frac{1}{2} mv^2 }$

Applying the moment of inertia of a sphere we have,

$\frac{KE_{Rotational} }{KE_{Translational}} = \frac{\frac{1}{2} (\frac{2}{5}mr^2)\omega^2 }{\frac{1}{2} mv^2 }$

$\frac{KE_{Rotational} }{KE_{Translational}} = \frac{2}{5} \frac{r^2\omega^2}{v^2}$

$\frac{KE_{Rotational} }{KE_{Translational}} = \frac{2}{5} \frac{(2.42*10^{-2})^2(158)^2}{23.3^2}$

$\frac{KE_{Rotational} }{KE_{Translational}} = 0.01077$

Therefore the ratio will be 0.01077

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The center of mass of a pitched baseball or radius 2.42 cm moves at 23.3 m/s. The ball spins about an axis through its center of mass with an angular speed of 158 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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