Rotational Energy Homework - Calculate Moment of Inertia & KE

AI Thread Summary
The discussion revolves around calculating the moment of inertia and rotational kinetic energy for a dancer spinning at 72 rpm. The participant uses the solid sphere and solid cylinder equations to compute the moment of inertia based on their body mass distribution: head (7%), arms (13%), and trunk and legs (80%). Initial calculations for the moment of inertia yield a total of 65190, but the participant later realizes an error in their approach. The focus is on applying the correct formulas and measurements to achieve accurate results. The conversation highlights the importance of careful calculation in physics problems related to rotational motion.
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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!
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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