How much rotational kinetic energy does the disk have ?

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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 rad/s. The force applied to the string is 9 N, and the center of mass has moved 0.11 m while the hand has moved 0.28 m. The moment of inertia of the disk can be derived using the formula for rotational kinetic energy, which is defined as \( KE_{rot} = \frac{1}{2} I \omega^2 \), where \( I \) is the moment of inertia and \( \omega \) is the angular speed.

PREREQUISITES
  • Understanding of rotational dynamics
  • Familiarity with the concept of moment of inertia
  • Knowledge of angular velocity and its units
  • Basic principles of work and energy
NEXT STEPS
  • Calculate the moment of inertia for the disk using \( I = \frac{KE_{rot}}{\omega^2} \)
  • Explore the relationship between linear and angular motion
  • Study the effects of varying mass distribution on moment of inertia
  • Investigate the principles of energy conservation in rotational systems
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Physics students, mechanical engineers, and anyone interested in understanding rotational motion and energy calculations.

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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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