Explanation of Torque in the precession of a top.

[student335]

Homework Statement

I'm reading through Taylor's Classical Mechanics, and I am confused by one sentence in section 10.6

The image he is referencing is this

while the text is here.

Specifically the statement "the gravitational torque is clockwise"

Using the right hand-rule, I run my fingers along the e3 vector and curl down for gravity, so my thumb points into the screen, which is exactly what Taylor says when the torque vector is into the page. This means that, if I am looking at the top from above (the z-axis) I will see it rotating in the counterclockwise direction. This all I understand.

But what is he talking about when he says the gravitational torque is clockwise?

 

[TSny]

I agree, the wording is not entirely clear. Maybe he means that if the top were not spinning and you released the top from rest in the position shown, then the gravitational torque would cause the top to fall in the direction of increasing θ. That is, the top would rotate about the origin in the clockwise direction from our point of view. But, of course, the spinning top does not fall appreciably and, instead, precesses couterclockwise around the z axis from the point of view of looking down on the top from above if $\vec{\omega}$ is along e₃.

 

[student335]

That's what I thought too. The way we're looking at the top in the picture, if it dropped it would fall in a clockwise direction (assuming it was connected to the origin).

Thank you!