# Spinning up a progressively smaller sphere

• csmcmillion
In summary: He is a world-renowned physicist. Nonetheless, (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%

#### csmcmillion

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!

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.

## What is meant by "spinning up a progressively smaller sphere"?

"Spinning up a progressively smaller sphere" refers to the process of increasing the rotation speed of a sphere while decreasing its size. This can be achieved by applying torque to the sphere, causing it to rotate faster and faster as it becomes smaller and smaller.

## What is the significance of studying the spinning up of progressively smaller spheres?

Studying the spinning up of progressively smaller spheres can provide valuable insights into the behavior of rotating objects in different size scales. It can also help us understand the effects of rotation on the physical properties of matter, such as mass distribution and angular momentum.

## What factors affect the spinning up of progressively smaller spheres?

The spinning up of progressively smaller spheres is affected by various factors, including the initial rotation speed, the amount of torque applied, the size and shape of the sphere, and the medium in which the sphere is rotating (e.g. air, water, vacuum).

## What are some potential applications of studying the spinning up of progressively smaller spheres?

The knowledge gained from studying the spinning up of progressively smaller spheres can have practical applications in fields such as spacecraft design, fluid dynamics, and material science. It can also help us better understand natural phenomena, such as the formation of planets and stars.

## Are there any limitations or challenges to studying the spinning up of progressively smaller spheres?

One limitation of studying the spinning up of progressively smaller spheres is the difficulty in accurately measuring the rotation speed of very small objects. Additionally, the effects of other factors, such as air resistance, can make it challenging to isolate and study the specific effects of spinning up a smaller sphere.