How much rotational kinetic energy does the disk have ?

AI Thread Summary
The discussion focuses on calculating the rotational kinetic energy of a disk with a mass of 2.1 kg and an angular speed of 7.5 rads/s, given a constant pulling force of 9 N. Participants seek to understand the concept of rotational kinetic energy relative to the center of mass and the implications of the disk's moment of inertia. The center of mass has moved 0.11 m while the hand has moved 0.28 m, indicating a relationship between linear and rotational motion. Relevant equations for rotational kinetic energy and moment of inertia are discussed, with participants attempting to derive values based on the provided parameters. The thread emphasizes the importance of understanding these concepts in the context of rotational dynamics.
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A string is wrapped around a disk of mass 2.1 kg (it's density doesn't have to be uniform). From rest, you pull the string with a constant force of 9 N. At this instant, the center of mass has moved 0.11 m, and your hand has moved 0.28 m.

1. At this instant, how much rotational kinetic energy does the disk have relative to its center of mass?

2. At this instant, the angular speed of the disk is 7.5 rads/s. What is the moment of inertia of the disk?
 
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Relevant equations? Attempt at solution? Your thoughts?
 
Exactly what is meant by rotational kinetic energy "relative to the center of mass"?
 
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