Kinetic Energy in Rotational Motion Problem

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SUMMARY

The discussion revolves around calculating the rotational kinetic energy of a flywheel shaped as a uniform solid disk with a radius of 1.30 m and mass of 72.0 kg. The maximum radial acceleration allowed is 3600 m/s², leading to an angular velocity of 52.6 rad/s. The moment of inertia is calculated as 122 kg·m², resulting in a computed kinetic energy of 1.68 x 10^5 J. However, the correct kinetic energy is 8.42 x 10^4 J, highlighting the importance of the factor (1/2) in the rotational kinetic energy formula, K = (1/2)Iω².

PREREQUISITES
  • Understanding of rotational motion concepts
  • Familiarity with the moment of inertia for solid disks
  • Knowledge of angular velocity calculations
  • Proficiency in using the rotational kinetic energy formula
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  • Study the derivation of the moment of inertia for various shapes
  • Learn about the relationship between linear and angular acceleration
  • Explore advanced applications of rotational kinetic energy in engineering
  • Investigate the effects of radial acceleration limits on flywheel design
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itsme24
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Ok the problem is:

Energy is to be stored in a flywheel in the shape of a uniform solid disk with a radius of 1.30 m and a mass of 72.0 kg. To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 3600 m/s^2.

What I did was solve for the angular velocity through the radial acceleration:

3600m/s^2 = rw^2

w = 52.6 rad/s

Then I solved for the moment of inertia:

I = mr^2 = 72.0kg(1.30m)^2 = 122 kg*m^2

Finally I plugged it all into the rotational kinetic energy equation:

K = (1/2)(122m*m^2)(52.6rad/s)^2 = 1.68*10^5 J

The actual answer is 8.42*10^4, exactly half of what I got. I don't suppose someone could explain where the *(1/2) is coming from?
 
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The moment of inertia of a disk is?
 
hehe (1/2)mr^2
 
Energy is to be stored in a flywheel in the shape of a uniform solid disk with a radius of = 1.16m and a mass of 73.0 kg. To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 3510 m/s^2.

CAN SOMEONE PLEASE SOLVE THIS FFS IVE TRIED SO MANY OPTIONS AND ITS NOT WORKING!@@!_#!@#!@!@#)!@(#*)!@(#)((!@*
 

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