Rotational Kinetic Energy Problem

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SUMMARY

The discussion focuses on calculating the rotational kinetic energy and total kinetic energy of a thin uniform-density rod with a mass of 3.8 kg and a length of 3.0 m, rotating at an angular speed of 34 radians/s. The correct rotational kinetic energy is determined to be 1650 J, while the total kinetic energy is 1840 J. The moment of inertia for the rod is correctly identified as ml²/12 about its center of mass, which is crucial for accurate calculations.

PREREQUISITES
  • Understanding of rotational dynamics and kinetic energy
  • Familiarity with the moment of inertia formula for a uniform rod
  • Knowledge of angular velocity and its relationship to linear velocity
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the moment of inertia for various shapes
  • Learn how to apply the rotational kinetic energy formula Krot = 1/2 I ω²
  • Explore the relationship between linear and angular motion
  • Investigate energy conservation in rotational systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of rotational energy 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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