Gyroscopic motion question?

[khfrekek92]

Homework Statement

an apparatus consists of bicycle wheels A and B (assume I=mR^2) connected by a long rod with a pivot point at point C. wheel A is .8m away from pivot point, weight 3 kg, and has radius .4m. Wheel B is .8m from pivot point, weighs 2kg, and has radius .5m. Wheel B is spinning at 10 rad/sec clockwise as seen from A, and the entire thing precesses as seen prom above with a period of 2 sec. What is the angular velocity (and direction) of wheel A?

Homework Equations

I=mR^2, torque, J

The Attempt at a Solution

After finding the net torque on the system l2m2 (in the out direction) -l1m1 (in the out direction), i plugged numbers in and got 10.78 (out direction) for the net torque.

Then, as derived, it can be seen that J=torque/pi, so you get J=3.43 (out direction). which also equals I_A(omega)_A + I_B(omega)_B which I plugged everything into and got that the angular velocity of A is 3.27 rad/sec in what I'm guessing the counter clockwise direction as seen from B? Am I doing this right? and did I get the right answer?

Thanks in advance!

 

[mark726]

Thank you for your question. Based on the information provided, your solution seems to be correct. The net torque on the system is indeed 10.78 (out direction) and J=3.43 (out direction). The angular velocity of wheel A is 3.27 rad/sec in the counter clockwise direction as seen from B. This makes sense as wheel B is spinning clockwise, causing the entire system to precess in the opposite direction, thus resulting in wheel A's angular velocity being counter clockwise.

I would suggest double checking your calculations and units to ensure accuracy, but overall your approach and answer seem to be correct. Keep up the good work!



Scientist