Comparison between two Tippe tops

[abrahamabraham]

Homework Statement

Given two Tippe top (https://en.wikipedia.org/wiki/Tippe_top) that are made of the same material. The mass (and weight) of the first one is 2 times greater than the second. Given they have the same initial energy. Which of them will spin on its narrow stem first, and which of them will stop first (due to friction and energy loss)? This is a question I invented.

Relevant Equations

Please help me if there are any relevant equations.

I think that the second tippe top will spin on its stem first, and the first tippe top will stop spinning first due to its greater mass and lower angular velocity. Here are my ideas:

• They are given the same initial energy. By the conservation of energy principle, an object with greater mass would have lower angular velocity than one with smaller mass, if their initial energies are the same.
• For a tippe top to spin on its narrow stem, it needs to attain a critical angular velocity to overcome the friction at the point of contact.
• The one with smaller mass (the second tippe top) would attain a higher angular velocity compared to the one with greater mass, given they have the same initial energy.
• Therefore, the second tippe top (with smaller mass) will spin on its narrow stem first.
• Additionally, the top with greater mass would lose energy to friction faster compared to the one with smaller mass, since its angular velocity is lower.
• Therefore, the first tippe top (with greater mass) will stop spinning due to friction and energy loss sooner than the second tippe top.
  
  Am I right?

 

[haruspex]

They are given the same initial energy. By the conservation of energy principle, an object with greater mass would have lower angular velocity than one with smaller mass, if their initial energies are the same.

The conclusion is true, but it has nothing to do with energy conservation.

For a tippe top to spin on its narrow stem, it needs to attain a critical angular velocity to overcome the friction at the point of contact.

The friction at point of contact is what leads to standing on the stem. How does it present a barrier to be overcome?

• The one with smaller mass (the second tippe top) would attain a higher angular velocity compared to the one with greater mass, given they have the same initial energy.
• Therefore, the second tippe top (with smaller mass) will spin on its narrow stem first.

You do not offer any reason that the process would be faster. Even if your preceding point were correct, it only says there is a critical energy per unit mass for it to reach the upright position. It says nothing about how quickly it happens.

• Additionally, the top with greater mass would lose energy to friction faster compared to the one with smaller mass, since its angular velocity is lower.

I would have thought that the one with slower spin would slide a shorter distance against the surface in a given time, so lose energy more slowly.

• Therefore, the first tippe top (with greater mass) will stop spinning due to friction and energy loss sooner than the second tippe top.
  
  Am I right?

I don't see that you can reach an answer to this question by such handwaving. You need to deal with the equations.