Vertical force exerted by a spinning non-perpendicular gyroscope

[aeroseek]

A wooden box on a weighing scale weighs 1 kg. Inside the box is a gyroscope which is set spinning, and the box is now tilted at 45 degrees to the vertical and maintains this position due to the gyroscope inside.

What is the weight shown on the scale - is it 1 kg or less than 1 kg? Why is this?

Some contradictory answers here:

http://physics.stackexchange.com/questions/33866/does-a-toy-top-weigh-less-when-it-is-spinning

 

[Doc Al]

Why would you think it would weigh less?

 

[Dale]

Apply Newtons laws. What is the acceleration of the center of mass? What force is required to make that acceleration?

 

[A.T.]

Watch this video:

https://www.youtube.com/watch?v=GeyDf4ooPdo

https://www.youtube.com/watch?v=tLMpdBjA2SU

 

[Doc Al]

Great video A.T.! Thanks for posting. (Be sure to view the follow up explanatory videos. I remember the nonsense from Laithwaite some years back.)

 

[aeroseek]

Great video - I guess you guys can answer anything! Granted the gyroscope does not weigh less.

The question is then what effect does the gyroscope exhibit and why?

I used to simplify its effect as the following rule - push on the rim of a gyroscope and the force travels 90 degrees along the rim of the gyroscope in the direction of rotation before manifesting itself - any force takes effect not at the point of action but some place further along the rim - regardless of rotational speed? Why?