Rotational Kinetic Energy Problem

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The discussion revolves around calculating the rotational and total kinetic energy of a rotating rod with given mass and angular speed. The correct formula for rotational kinetic energy is Krot = 1/2 I ω², where I is the moment of inertia. The moment of inertia for a uniform rod rotating about its center is I = ml²/12. Participants clarify that the initial formula used was incorrect, leading to confusion in obtaining the correct answers, which are 1650 J for rotational kinetic energy and 1840 J for total kinetic energy. The conversation emphasizes the importance of using the correct moment of inertia formula for accurate calculations.
Loppyfoot
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Homework Statement



A thin uniform-density rod whose mass is 3.8 kg and whose length is 3.0 m rotates around an axis perpendicular to the rod, with angular speed 34 radians/s. Its center moves with a speed of 10 m/s.

(a) What is its rotational kinetic energy?
(b) What is its total kinetic energy?


Homework Equations



Well I know that Krot= 1/2I* w2. But when I try to use this equation, I get the wrong answer. I also know that I= 1/2mr^2

The correct answers are:

(a)= 1650 J
(b)= 1840 J

Does anyone have any idea on where I'm going wrong?

The Attempt at a Solution

 
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Loppyfoot said:
I also know that I= 1/2mr^2

from where did you get this?
 
Moment of Inertia= mr^2. Sorry.
 
How did you get that?
 
That's not the equation? Then what equation would I use to represent the rod with moment of inertia?
 
moment of inertia of a uniform rod is ml^2/12 about its center of mass.
 

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