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The Gyroscope Forum |
29 November 2024 01:44
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Welcome to the gyroscope forum. If you have a question about gyroscopes in general,
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Question |
| Asked by: |
Tim Bridle |
| Subject: |
Spherical Gyroscopes |
| Question: |
Hi all,
Was quite a gyroscope fan as a child, and have had a renewed interest in them for the last few years due to the hand gyroscopes, or Powerballs, that you can buy at sports or gadget stores. I've got loads of these Powerballs at home, and the physics behind them fascinates me. I think I understand the basics of how they work.
However, have got to thinking recently about whether a completely spherical gyroscope would work as a Powerball rotor. I was under the impression that the more "wheel"-shaped a gyroscope rotor is, the greater the gyroscopic torque that is produced. A standard Powerball rotor weighs something like 200g, but can create 20Kg of torque at 15000rpm. (Apparently.)
What sort of torque would a completely spherical rotor, also weighing 200g, create at 15000rpm? |
| Date: |
3 June 2008
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Answers (Ordered by Date)
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| Answer: |
dommie - 20/02/2009 17:25:08
| | | You will need to know the polar moment of inertia for the rotor ( I ),
also the angular velocity of precession ( wp ) [radians/sec],
and the spin velocity ( W )= rpm x 2pi / 60 [radians/sec],
[remember use the SI system of units > kg metre second radian newton etc]
Now-------- T [Nm] = I [kg.m sqd.] x W x wp
You will have to work out the radius of the 0.2 kg sph. rotor [start with the density of its material] , that done, now you can calculate the polar moment of inertia for the rotor.
The formula for the polar moment of inertia of a sphere is-----
I = (2/5) x M[0.2kg] x r squared [m]
With a Powerball there may be other factors to consider eg. accn. of rotor
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| Answer: |
dsfa - 25/08/2009 05:52:45
| | | I'm not sure if the shape affects the torque as much as the mass of the rotor. The shape obviously has to be circular but I think it will have little effect to complete the sphere.
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