How Is the Direction of Gyroscope Precession Determined?

[rleung3]

Hi,

It asks me to state whether the direction of the gyroscope precession is clockwise or counterclockwise (see attachment). I am confused as to how they determined from the top view (on the left) that the direction of angular velocity and angular momentum were pointing towards the left. They don't explain it at all.

Any thoughts would be greatly appreciated. Thanks so much!

Ryan

 

[berkeman]

Is there a vector equation that describes the precession?

If your book doesn't have it, maybe this wikipedia article will help (or you can google precession):

http://en.wikipedia.org/wiki/Precession

 

[rleung3]

Hmmm, nope, there isn't any equation that describes a vector for precession.

 

[OlderDan]

Hmmm, nope, there isn't any equation that describes a vector for precession.

The diagram on the left is perhaps confusing. The ω shown there is not the vector ω. It is showing the direction of rotation of the wheel. The direction of the ω vector is along the axis of rotation, in a right-hand sense. The arrow labeled ω in the diagram on the right is in the proper direction. For objects spinning on a symmetry axis, the angular momentum L is in the direction of ω as shown in the digram. An applied torque causes the angular mometum to change in the direction of the torque at a rate that is equal to the torque. As L changes direction, ω also changes direction and remains parallel to L.

Torque is also a vector whose direction is along an axis. To produce the torque shown in the diagram, you would have to push the right hand side of the wheel axle into the page, or pull the left side out of the page, or do both at the same time.

The change in angular momentum shown in the diagram is very exaggerated, but it shows that the direction of L changes in response to the applied torque without changing the magnitude of L. As soon as L changes a little bit, everything else changes direction too. The L vector sweeps around with constant length, and the ω vector also sweeps around with constant length. This phenomenon is called precession.

 

[physics girl phd]

Nice explanation above! I'd add in that I'd stick a doughnut on a straw and think of how it spins as you hold one end of the straw stationary and let the doughnut roll on the table. Good excuse for a doughnut study session. :)

 

[rleung3]

Thanks so much OlderDan.

So, the thing I am still confused on now is...can you look at the diagram on the left and automatically "translate" it into the diagram on the right-hand side? The book gives off the impression that you can, but I am confused as to how.

Thanks again.

Ryan

 

[OlderDan]

Thanks so much OlderDan.

So, the thing I am still confused on now is...can you look at the diagram on the left and automatically "translate" it into the diagram on the right-hand side? The book gives off the impression that you can, but I am confused as to how.

Thanks again.

Ryan

There is nothing in the diagram on the left to show that a torque is being applied. If they told you about the torque, then you could create the diagram on the right.

 

[BobG]

Making sure you're considering the right point of view in definitions can be tough. Sometimes it's easier to use your hands (the drawback to this is that they'll make Dilbert cartoons about you).

From the pivot point (the supported part of the gyroscope), curl your fingers in the same direction the gyroscope is spinning. Your thumb will be pointing the same direction as the angular momentum vector (it will be pointing away from the pivot point or towards the pivot point).

The direction the gyro precesses is the same direction as the cross product of the angular momentum vector and the force of gravity. The force of gravity is down. The angular momentum vector is your reference vector (you want to find out how it changes from its original orientation).

With forearm and hand pointing the same direction as the angular momentum vector, curl your fingers from the angular momentum vector to the gravitational vector. Your thumb points the same direction that the angular momentum vector will move around the base.

If the gyro is rotating clockwise as you look from the base up the axis of the gyro, then the gyro precesses counter clockwise as you look down from above. If the gyro is rotating counter-clockwise as you look from the base up the axis of the gyro, the gyro precesses clockwise as you look down from above.

(Technically, Older Dan is right, but if you do this experimentally, gravity is the one torque that will be sure to act on your gyroscope. Generally speaking, you do need to know where the torque acting on your gyro is coming from.)