Feynman Exercises 19-1: Metal rod framework being pulled in while spinning

In summary: So maybe it's just old.In summary, the conversation discusses the moment of inertia before and after a collapse, as well as the conservation of angular momentum. It is noted that the moment of inertia of the mechanism remains unchanged, but the framework may change. There is also a discrepancy in the mass symbol used in the problem.
  • #1
aa_o
24
4

Homework Statement


upload_2018-5-30_20-1-21.png


Homework Equations


961d11c880763ec91d800f29aa48d57dff4844cd

aa5bad8dd9fbe093f71a9f3887a229701a625271


The Attempt at a Solution



The moment of inertia before collapse is for each rod:
BEFORE COLLAPSE:[/B]
Ib = ∫(L2 + x2) dm = m/L ∫(L2 + x2) dx = 4/3 * m * L2
We have 8 of these plus the inertia of the mechanism, giving a total I,
It = 8 * Ib + Ik = (32/3 * m * + 40/3 * M) * L^2
The energy is thus:
Tb = 1/2 * It* ωo2
AFTER COLLAPSE:
Ia = ∫(x2) dm = m/L ∫(x2) dx = 1/3 * m * L2
And the mechanism is the same:
So we have total of:
It_a = 8 * Ia + Ik = (8/3 * m * + 40/3 * M) * L2
The energy is now:
Ta = 1/2 * It_a * ωo2
And energy difference must be:
Ta - Tb = 1/2 * ωo2 * m * (8 / 3 - 32/3) * L2 = -ωo2 * m * 4 * L2

But the solution stated is: ωo2 * M * 6 (note the difference in mass symbol)
What am i doing wrong?
 

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  • #2
Why is the angular speed unchanged through the collapse?
 
  • #3
kuruman said:
Why is the angular speed unchanged through the collapse?
Because the moment of inertia of the mechanism is unchanged. Since I = L / ω (L is the angular momentum here!).

But maybe I've been to quick in that assumption. All I know is that I is constant for the mechanism - not that L or ω is constant. Am I on the right track?
 
  • #4
aa_o said:
Because the moment of inertia of the mechanism is unchanged. Since I = L / ω (L is the angular momentum here!).

But maybe I've been to quick in that assumption. All I know is that I is constant for the mechanism - not that L or ω is constant. Am I on the right track?
Sure the moment of inertia of the mechanism is unchanged, but what about the framework? Is that also unchanged? Your expressions for It and It_a are not the same. In fact It_a < It which means that the contraption will speed up much like a spinning skater when she pulls her arms in.,
 
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  • #5
kuruman said:
Sure the moment of inertia of the mechanism is unchanged, but what about the framework? Is that also unchanged? Your expressions for It and It_a are not the same. In fact It_a < It which means that the contraption will speed up much like a spinning skater when she pulls her arms in.,
Ahh, okay. There's conservation of angular momentum. I'll work it out and return with what i got.
 
  • #6
aa_o said:
Ahh, okay. There's conservation of angular momentum. I'll work it out and return with what i got.
That's an excellent way to proceed. Note: To get the answer you think is correct, you must set ##m=M##.
 
  • #7
kuruman said:
That's an excellent way to proceed. Note: To get the answer you think is correct, you must set ##m=M##.
Ahh yes! Thanks a lot. Quick last question: Do you know if the different symbol for mass is a mistake in the problem? Or am i missing some connection?

To anyone else stuck here:

Just note that angular momentum is conserved, meaning: I_t * ω_0 = I_t_a * ω_a (ω_a is angular velocity after collapse). After this, it's just algebra.
 
  • #8
aa_o said:
Ahh yes! Thanks a lot. Quick last question: Do you know if the different symbol for mass is a mistake in the problem? Or am i missing some connection?
I have no idea. Probably a typo by whoever transcribed the problem or by somebody who didn't pay attention to the difference between upper and lower case characters. It looks like the question was typed using a typewriter, a technology that faded about 30 years ago.
 

1. What is the purpose of the "Feynman Exercises 19-1" experiment?

The purpose of the "Feynman Exercises 19-1" experiment is to demonstrate the phenomenon of gyroscopic precession, which occurs when a spinning object experiences a change in its orientation when a force is applied in a different direction.

2. How is the metal rod framework being pulled in during the experiment?

The metal rod framework is being pulled in by a string attached to one end of the rod and pulled by a person at the other end.

3. What happens to the metal rod framework as it is pulled in?

As the metal rod framework is pulled in, it experiences a change in its orientation due to the force of the string pulling it in a different direction. This causes the rod to precess, or rotate, around its axis.

4. Why does the metal rod framework spin while being pulled in?

The metal rod framework spins due to the conservation of angular momentum. As the rod is pulled in, its rotational speed increases in order to conserve its angular momentum, resulting in the spinning motion.

5. What can we learn from the "Feynman Exercises 19-1" experiment?

The "Feynman Exercises 19-1" experiment teaches us about the principles of angular momentum and gyroscopic precession. It also demonstrates how forces can affect the orientation and motion of objects in motion, as well as the concept of conservation of energy. These principles have practical applications in fields such as engineering and physics.

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