Does a Spinning Top Exhibit Bobbing Motion?

[sclatters]

Homework Statement

http://i42.tinypic.com/20adicz.jpg

Homework Equations

torque=rxF
angular precession velocity=Δtheta/Δt
assume that Δtheta=ΔL/Lsin(theta)

The Attempt at a Solution

I can conclude that the subsequent motion of the top will be an anti-clockwise circle about the origin but would there be a bobbing motion? My answer for part a) just shows the spinning top making this circle. Do you think this is what the question is asking for?

For part b) I have worked out that the angular procession velocity=mgd/Iω so would the frequency=mgd/2∏Iω? Does this answer sit alongside the statement of "using the variables given" even though there is no direct mention of I?

 

[Doc Al]

I can conclude that the subsequent motion of the top will be an anti-clockwise circle about the origin but would there be a bobbing motion? My answer for part a) just shows the spinning top making this circle. Do you think this is what the question is asking for?

Yes.

For part b) I have worked out that the angular procession velocity=mgd/Iω so would the frequency=mgd/2∏Iω?

The angular velocity of precession is the angular frequency.

Does this answer sit alongside the statement of "using the variables given" even though there is no direct mention of I?

No. Express I in terms of the variables given.

 

[sclatters]

Great, thanks!

I am a little unsure on how to express I in terms of the variables given though?

 

[Doc Al]

I am a little unsure on how to express I in terms of the variables given though?

What's the moment of inertia of a disk? You are given the mass and radius.

 

[sclatters]

Of course, Ma²/4. Thank you very much for your help again!

 

[Doc Al]

Of course, Ma²/4.

Almost.

 

[sclatters]

I'm not sure why it isn't (ma^2)/4? Do I need to use the parallel axis theorem to find the moment of inertia in another position? Maybe at the point the spinning top intercepts the origin O?

 

[Doc Al]

I'm not sure why it isn't (ma^2)/4?

Where does the 4 come from?

 

[sclatters]

Sorry, I was thinking about the x and y components. They both equal (ma^2)/4 and the z component equals the x and y components added together. This gives the moment of inertia to be (ma^2)/2 straight through the disk as if it were spinning like a CD. Is this correct?

 

[Doc Al]

Sorry, I was thinking about the x and y components. They both equal (ma^2)/4 and the z component equals the x and y components added together. This gives the moment of inertia to be (ma^2)/2 straight through the disk as if it were spinning like a CD. Is this correct?

Yes, now you've got it.