Explanation of Torque in the precession of a top.

In summary, the conversation discusses the confusion surrounding the statement "the gravitational torque is clockwise" in section 10.6 of Taylor's Classical Mechanics. The participants agree that the wording is unclear and suggest that it may refer to the direction in which the top would fall if released from rest in the position shown. However, since the top is spinning and does not fall, it instead precesses counterclockwise around the z-axis. The participants also note that if the top were to fall, it would fall in a clockwise direction from the point of view of looking down on the top from above.
  • #1
student335
7
0

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
1m822Pk.png


while the text is here.
1jUcx3c.png


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?
 
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  • #2
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.
 
  • #3
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!
 

1. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis or pivot point. It is a vector quantity, meaning it has both magnitude and direction.

2. How is torque related to the precession of a top?

Torque is the driving force behind the precession of a top. When the top is spinning, its angular momentum creates a force that causes it to precess, or rotate around a vertical axis.

3. What factors affect the amount of torque in the precession of a top?

The amount of torque in the precession of a top is affected by the mass of the top, the speed at which it is spinning, and the distance between the top's center of mass and its pivot point. Additionally, external forces such as friction or air resistance can also affect the torque.

4. How does torque differ from force?

While both torque and force are measures of the interaction between two objects, force is a linear concept that causes an object to accelerate in a straight line, while torque causes an object to rotate around an axis.

5. Can torque be positive or negative?

Yes, torque can be either positive or negative. A positive torque causes an object to rotate in a certain direction, while a negative torque causes it to rotate in the opposite direction. The direction of the torque vector is determined by the direction of the force causing the rotation.

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