Rotational Energy Homework - Calculate Moment of Inertia & KE

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SUMMARY

The discussion focuses on calculating the moment of inertia and rotational kinetic energy for a dancer spinning at 72 rpm. The participant used the equations for a solid sphere and a solid cylinder to derive the moment of inertia based on body mass distribution: head (7%), arms (13%), and trunk/legs (80%). The calculations yielded a total moment of inertia of 65190 kg·cm², with individual contributions from the head, arms, and trunk calculated using specific formulas. The participant identified an error in their initial calculations but later corrected it.

PREREQUISITES
  • Understanding of rotational dynamics and moment of inertia
  • Familiarity with the equations for solid shapes (sphere and cylinder)
  • Basic knowledge of mass distribution in the human body
  • Ability to perform unit conversions (e.g., cm to m)
NEXT STEPS
  • Research the application of the parallel axis theorem in rotational dynamics
  • Learn about the calculation of rotational kinetic energy using the formula KE = 1/2 I ω²
  • Explore the effects of body position on moment of inertia in sports science
  • Investigate advanced topics in biomechanics related to rotational motion
USEFUL FOR

Students studying physics, particularly in mechanics, athletes interested in biomechanics, and anyone involved in dance or sports performance analysis.

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Homework Statement


A dancer spinning at 72 rpm about an axis through her center with her arms outstretched. The distribution of mass in a human body is
Head: 7%
Arms 13%
Trunk and legs: 80%
Using your own measurements on your body calculate your
a) moment of inertia about your spin
b) rotational kinetic energy

Homework Equations


I decided to use two equations: the solid sphere and solid cylinder
I=2/5 MR^2
I=1/2 MR^2

The Attempt at a Solution



75 kg for weight, 10 cm for head, 60 cm for arms, 90 cm for trunk.

.07*75=5.25
.13*75=9.75
.8*75=60

Head: 2/5*(5.25)(5)^2=52.5
Arm: 1/2*(9.75)*(30)^2=4387.5
Trunk: 1/2(60)(45)^2=60750
I add those up and got 65190I'm not sure if I did this right.
 
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Never mind, I saw what I did wrong!
 

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