Total energy of a rolling sphere

AI Thread Summary
The total energy of a rolling solid sphere with a mass of 1.0 kg and a translational speed of 10 m/s is calculated to be 70 Joules. This total energy combines both rotational kinetic energy and linear kinetic energy, confirming that KE_total equals KE_rot plus KE. The rotational kinetic energy is derived using the moment of inertia formula, resulting in 20 Joules, while the linear kinetic energy calculation yields 50 Joules. Translational velocity refers to the speed of the sphere's center of mass, which is consistent with its directional movement. Understanding these concepts is crucial for solving problems related to rolling motion.
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Homework Statement


A solid sphere has a mass of 1.0 kg. It is rolling at a translational speed of 10 m/s. What is the total energy of the rolling sphere?
I think I got the problem but I'm not sure I went about it the right way.

Homework Equations


I = (2/5)mr^2
KE_rot = (1/2)Iw^2
KE = (1/2)mv^2

The Attempt at a Solution


I assumed KE_total = KE_rot + KE...which I'm not sure is right.
So...
KE_rot = (1/2)Iw^2 = (1/2)(2/5)(m)(r^2)(w^2) = 20 Joules
and...
KE = (1/2)(m)(v^2) = 50 Joules
soo...

KE_total = 70 Joules
This is the right answer, but I'm not sure if the total kinetic energy is actually the rotational kinetic energy plus the linear kinetic energy. Also...what is translational velocity? Is this any different than the sphere moving in a direction?
 
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I assumed KE_total = KE_rot + KE...which I'm not sure is right.

That's right.

The translational velocity is the velocity of the center of mass.

The rotational energy is about an axis through the center of mass.
 
Here is a link that touches on rolling motion if you are interested in further study:
http://dept.physics.upenn.edu/courses/gladney/mathphys/java/sect4/subsubsection4_1_4_3.html

(Page down to rolling motion section.)
 
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