Angular acceleration of a falling arm

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  • #1

Homework Statement



Assume your arm is a solid rod, 0.740 m in length, free to rotate about your shoulder (so its
moment of inertia is (1/3)ML^2). If you hold your arm out sideways, and then completely relax
your muscles, what is the initial downward angular acceleration of your arm?

Homework Equations


τ=LF=Iα
F=mg
I=(1/3) ML^2

The Attempt at a Solution


I'm not given a specific formula to use, but I think the above formula for Torque applies. I'm not using conservation of energy because I dont have a value for the height to use for potential energy.

If I plug the formulas for inertia and Fg into the torque formula:

Lmg=(1/3)ML^2 α

α=3g/L = (3*9.81)/0.740 = 39.77 but the answer key says the answer is 19.9 (half).


What am I doing wrong here?
 
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Answers and Replies

  • #2
SammyS
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Homework Statement



Assume your arm is a solid rod, 0.740 m in length, free to rotate about your shoulder (so its
moment of inertia is (1/3)ML^2). If you hold your arm out sideways, and then completely relax
your muscles, what is the initial downward angular acceleration of your arm?

Homework Equations


τ=LF=Iα
F=mg
I=(1/3) ML^2

The Attempt at a Solution


I'm not given a specific formula to use, but I think the above formula for Torque applies. I'm not using conservation of energy because I dont have a value for the height to use for potential energy.

If I plug the formulas for inertia and Fg into the torque formula:

Lmg=(1/3)ML^2 α

α=3g/L = (3*9.81)/0.740 = 39.77 but the answer key says the answer is 19.9 (half).

What am I doing wrong here?
What is the location of the center of mass of the arm ?
 
  • #3
L/2, the very center of the length?
 
  • #4
SammyS
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L/2, the very center of the length?
Yes.

That's where gravity effectively acts.

So, what is the torque produced by gravity about the shoulder ?
 
  • #5
τ=(L/2)F=(L/2)mg
But the value of the length in the formula for inertia will remain the full length right??
 
  • #6
SammyS
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τ=(L/2)F=(L/2)mg
But the value of the length in the formula for inertia will remain the full length right??
Right !
 
  • #7
awesome!! Thank you so much for the help!!
 
  • #8
SammyS
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awesome!! Thank you so much for the help!!
You're welcome.

By The Way, welcome to PF !
 
  • #9
Thanks!
 

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