- #1
Mantella
- 10
- 0
I was hoping someone could clear this up for me. I've been thinking about it a bit, and I am thoroughly confused. Here is what I have come up with so far.
The situation: A horizontal (wheel vertical) gyroscope spinning counter clockwise held up at one end by a string. Now change views so we're looking down on it from above. Looks like •--|-- with • being the point where it's held up and --|-- being the gyroscope (from this angle the wheel looks like a line). Positive y and x are |_ respectively (positive z is out of the page).
My thoughts:
Angular momentum is in the positive x direction via right hand rule. The force of gravity is in the negative z direction and R is in the positive x direction, so using the cross product of R x F gets the positive y direction for the torque. So the gyroscope moves counterclockwise around the point where it's held up by the string.
For friction: The friction force will act on the wheel and point in the opposite direction of the tangential velocity of the wheel. For simplicity just think about this as if it where in the orientation of a skidding wheel. In this situation that direction is the negative y direction. For the friction force the R will be the radius of whatever it is acting on. Let's just say that the radius points in the negative z direction because this works for our purposes. R x F for friction gives us with a torque that points in the negative x direction. As we would expect it opposes the angular velocity.
But wait!
The torque from friction is in the x-y plane! The torque from gravity also acts in the x-y plane. How can the gyroscope drop into the negative z direction if its net torque has no z component? I can think of only two answers, air resistance supplies this downward torque or there is some underlying physics that I am unable to comprehend.
Air resistance:
The force from air resistance points in the negative y direction because the gyroscope moves counterclockwise, and it operates over an R that is in the positive x direction. The cross product of these vectors gives us a torque in the negative z direction.
If you kept a gyroscope in the orientation described in a vacuum would it forever remain "defying" gravity? That just seems wrong. There must be something else to it.
Sorry for the really long and confusingly phrased post...
-Alex
The situation: A horizontal (wheel vertical) gyroscope spinning counter clockwise held up at one end by a string. Now change views so we're looking down on it from above. Looks like •--|-- with • being the point where it's held up and --|-- being the gyroscope (from this angle the wheel looks like a line). Positive y and x are |_ respectively (positive z is out of the page).
My thoughts:
Angular momentum is in the positive x direction via right hand rule. The force of gravity is in the negative z direction and R is in the positive x direction, so using the cross product of R x F gets the positive y direction for the torque. So the gyroscope moves counterclockwise around the point where it's held up by the string.
For friction: The friction force will act on the wheel and point in the opposite direction of the tangential velocity of the wheel. For simplicity just think about this as if it where in the orientation of a skidding wheel. In this situation that direction is the negative y direction. For the friction force the R will be the radius of whatever it is acting on. Let's just say that the radius points in the negative z direction because this works for our purposes. R x F for friction gives us with a torque that points in the negative x direction. As we would expect it opposes the angular velocity.
But wait!
The torque from friction is in the x-y plane! The torque from gravity also acts in the x-y plane. How can the gyroscope drop into the negative z direction if its net torque has no z component? I can think of only two answers, air resistance supplies this downward torque or there is some underlying physics that I am unable to comprehend.
Air resistance:
The force from air resistance points in the negative y direction because the gyroscope moves counterclockwise, and it operates over an R that is in the positive x direction. The cross product of these vectors gives us a torque in the negative z direction.
If you kept a gyroscope in the orientation described in a vacuum would it forever remain "defying" gravity? That just seems wrong. There must be something else to it.
Sorry for the really long and confusingly phrased post...
-Alex