Rotation: Calculating Rotational Energy of Sphere with Steiner

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To calculate the rotational energy of a sphere rolling down a frictionless plane, the moment of inertia is given as I = 2/5*m*r^2. The formula for rotational energy is Erot = 1/2*I*w^2, where w is the angular velocity. The confusion arises regarding the application of Steiner's theorem, which is used to find the moment of inertia about an axis parallel to one through the center of mass. Generally, Steiner's theorem is applied when the axis of rotation is not through the center of mass, but for a sphere rolling without slipping, it is not necessary. Understanding when to apply Steiner's theorem is crucial for solving problems involving rolling objects.
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Homework Statement



Consider a spere with momenta of inertia of 2/5*m*r^2 that rolls down a plane surface (no friction). I want to calculate the rotational energy of the sphere when it has speed v0.

Homework Equations



Erot=1/2*I*w^2

The Attempt at a Solution



My only problem is: Do I need to transform my I=2/5*m*r^2 with the rule of steiner, or don't I have to use the rule of Steiner? I would say no.
 
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I'm so confused because sometimes Steiner's theorem isn't used and sometimes it is used for rolling objects. Can you please generalize, when I have to use Steiner's theorem for rolling objects? Would be really helpful.
 

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