Calculating Kinetic Energy of Rotating Bar

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The kinetic energy of a rotating bar can be calculated using the moment of inertia and angular velocity. If the bar has varying speeds along its mass, calculus may be necessary to determine the moment of inertia accurately. The formula for rotational energy is given as 1/2 I ω², where I is the moment of inertia and ω is the angular velocity. Understanding these concepts is essential for calculating the kinetic energy in such scenarios. Accurate calculations depend on the specific distribution of mass and the axis of rotation.
swechan02
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What would be the kenetic energy, it the bar is rotating? But it has different speed along it's mass. Need to use calculas?
 
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The short answer is "yes." You can roll it all up into a single package if you know (or can calculate) the moment of inertia about the axis of rotation in which case the rotational energy is \frac {1}{2} I \omega^2
 
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