Spinning up a progressively smaller sphere

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Discussion Overview

The discussion revolves around the relationship between the size of a spinning object and its moment of inertia, particularly in the context of a physics lecture that stated smaller diameters make it harder to spin up a given mass. Participants explore the implications of torque and moment of inertia, questioning the instructor's claim and examining the physics behind spinning objects.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant recalls that moment of inertia increases with the square of the radius, suggesting it should be easier to spin smaller objects.
  • Another participant references the behavior of ice skaters, arguing that reducing radius while maintaining mass allows for faster spinning, implying it becomes easier to spin.
  • A participant questions the instructor's statement, suggesting that if the radius approaches zero, it would indeed be difficult to spin, but also argues that torque decreases with radius while moment of inertia decreases with the square of the radius.
  • One participant presents a thought experiment comparing two systems of buckets of water tied with different rope lengths, arguing that the larger system requires more energy to spin up, thus making it "harder."
  • Another participant asserts that the instructor could be wrong or misunderstood, but emphasizes that the instructor is a credible source.

Areas of Agreement / Disagreement

Participants express disagreement regarding the instructor's claim, with some supporting the idea that smaller objects are easier to spin while others question the validity of the instructor's statement. The discussion remains unresolved with multiple competing views presented.

Contextual Notes

Participants reference specific physics concepts such as torque and moment of inertia, but there are unresolved assumptions regarding the definitions and implications of these terms in the context of the discussion.

csmcmillion
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I was watching a physics lecture and the instructor made the statement that "for a given mass, decreasing the diameter of the body makes it harder to spin up". In one way this makes sense, as with a smaller diameter one has a shorter torque arm to work with... however, I seem to recall from my physics that the moment of inertia goes as r^2. Which would say that it would be easier to spin up as the size decreases.

What am I missing?

Thanks!
 
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I think you are right.

Are you sure he did not say "makes it spin up harder", instead? That would make a lot of sense, that's what ice skater do...they have constant mass but when they reduce their radius (by bringing arms to the chest) they spin faster given the same energy...that means, it became easier to spin.
 
gsal said:
I think you are right.

Are you sure he did not say "makes it spin up harder", instead?

I'm sure. This was in a QM context and he was talking about how hard it is to give an electron a quantum of spin due to it's very small size.
 
Well...if it is THAT small, no wonder it is difficult...try to spin something with radius zero!

Nevertheless, (for a given force) torque will go down proportional to radius and moment of inertia will go down proportional to the square of the radius...so, I still think things get easier and easier.

If the radius goes down from 5 to 4, the torque decreases 20% but the moment of inertia went down from k25 to k16, that's 36%

no?
 
gsal said:
Well...if it is THAT small, no wonder it is difficult...try to spin something with radius zero!

Nevertheless, (for a given force) torque will go down proportional to radius and moment of inertia will go down proportional to the square of the radius...so, I still think things get easier and easier.

If the radius goes down from 5 to 4, the torque decreases 20% but the moment of inertia went down from k25 to k16, that's 36%

no?

Right but he (Susskind) explicitly says the Electron has a finite radius. I agree with your calculations. I'm still scratching my head over this.
 
I think your instructor is wrong or you misunderstood him. It would be easier to spin up a smaller object with same mass. Think about it, which one has more energy, two buckets of water tied together by a foot long rope and spun around the system's center of mass, or the same buckets tied together by a 10 foot rope and spun at the same speed? (If you cut the rope while spinning, which will make a bigger splash?) To start from rest and spin up the larger system would take more energy, and thus is "harder" (whatever that means).
 
chrisbaird said:
I think your instructor is wrong or you misunderstood him.

I'm sure I didn't misunderstand, as he stated it in two different (video) lectures. He could be wrong, but he (Susskind) is no lightweight.
 

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