Question

Conservation of angular momentum and gyro

http://www.youtube.com/watch?v=zLy0IQT8ssk

from time 23:00 to around the time he does the wheel gyro experiment.

Professor does two experiments.. one he holds the wheel and steers while sitting on a rotating stool (a)
and second hooks the rotating wheel to a rope (b) and he says they are the same thing.
now here is my understanding of this and i want to know if its right

Answer 1

i can look at exp a) in two ways..

first way.. i can take both the wheel and the professor with the stool as the system, in that case the torque put by professor is internal and hence angular momentum MUST BE CONSERVED.

Answer 2

so.. the way i see it, to make L the same, it has to cancel the y axis L and thus the system rotates in the negative y axis

my doubt is what about the decreased L along x axis?
what i thought was, since gravity and the chair does not allow the system to rotate along x axis, there is external torque

but if they were both in outerspace with no gravity.. i would predict both of them would not only rotate about y axis but also about x axis.. so is that right? thats my question 1

Answer 3

secondly.. professor mentions in the lecture, that both the experiment a and b are identical

i think to look at it that way, in experiment a i should consider only the WHEEL as my system, in which case, i understand that the torque put by professor is external and thus the angular momentum is chasing the torque. and they seem identical. but there is one difference, in exp b, the wheel does not tilt, but in a the wheel is tilted.. so whats the difference? - thats question 2

Answer 4

Still thinking about question 1, but I think I can help with question 2.



Looking at when the wheel is perpendicular to the ground in both experiments

in a) it is before the professor applies the torque; he's holding the rod the wheel spins around at both ends so he is doing all of the work against gravity to keep both ends parallel. There is no resultant torque.

in b) it's for the duration of the experiment. The wheel is only being held up at one end so gravity applies a constant external torque; it wants to make the wheel fall, but the angular momentum prevents it so "produces" a torque as a reactionary force. Notice that the wheel precesses clockwise from the bottom. Gravity is trying (unsuccessfully) to displace the wheel a positive angle from the verticle ----> |/ like that.

in a) the first torque the professor applies causes the wheel to displace a negative angle from the vertical like this ---- > \| opposite of what gravity tries to do, and thus he precesses anticlockwise from the bottom.




Does that either help or even make sense?