Solution"Review Problem Help for Physics Exam

[fball558]

Review problem help??

Homework Statement

Im finishing up studying for my physics exam tonight. i ran into a couple problems i did not know how to do, and the help room is packed. so i figured i would try here again seeing you guys know what your talking about just as much as them (if not better)
here is the problem, sorry it is so long

A standard bicycle wheel with extra mass
filling the tire is set spinning rapidly about a long axle.
(pretty much just a solid disk, they word it funny)
One end of this axle rested on a holder at the top of a
large mounting post, which allows the gyroscope to
rotate freely about the vertical post. The spinning
gyroscope was mounted on the post initially pointed
straight up, but gradually it tipped over and began
precessing about the vertical direction (meaning that the
spinning gyroscope was also sweeping out a circular
path in a horizontal plane).

A. Eventually the gyroscope axle is completely horizontal, similar to what is
shown in the figure, while precessing about the mounting post. In this configuration, list
the most significant forces acting on the gyroscope and describe the vector sum of these
forces.

B. The mass of the outer part of the bicycle wheel is 4.1 kg, the radius of the
wheel is 0.33 m, and the wheel is spinning at 6.0 revolutions per second. What is the
magnitude of the wheel’s angular momentum about its axle?

C. At a certain instant the angular momentum
of the wheel about its axle is exactly in the +x direction:
Lo = Lo ˆx. (The free tip of the axle is also pointing in this
direction.) The total length of the axle is 0.30 m, and the
wheel is attached at the midpoint. What is the torque on
the gyroscope about the end of the axle on the mounting
post?

D. At a time t=0.10 s later, what is the (approximate) angular momentum of the
wheel?

E. You have shown above what the direction of the torque due to gravity is,
and hence what direction the axle (and L) will move on account of the gravitational
torque. Can gravity cause the axle of the spinning bicycle wheel to tilt downwards (-y
direction)? Why or why not? Why doesn’t the wheel just fall down, the way a nonspinning
wheel would?

any help would be GREAT!

 

[jbsteele]

Homework Equations A. The most significant forces acting on the gyroscope are gravity and the force of the holder at the top of the mounting post. The vector sum of these forces would be directed downward and act in the opposite direction to gravity. B. The magnitude of the wheel's angular momentum is given by L = Iω, where I is the moment of inertia of the wheel and ω is its angular speed. Since the wheel is a solid disk, I = mr2, where m is the mass of the wheel and r is its radius. Therefore, the magnitude of the wheel's angular momentum is L = (4.1 kg)(0.33 m)2(6.0 s-1) = 1.23 kgm2s-1. C. The torque on the gyroscope about the end of the axle is given by τ = r × F, where r is the distance from the point of application of the force to the point of rotation and F is the net force acting on the gyroscope. For this problem, the force is due to gravity and is directed downwards. In this case, the torque is τ = 0.15 m × F = 0.15 m × mg, where m is the mass of the wheel and g is the acceleration due to gravity. D. At time t=0.10 s later, the angular momentum of the wheel is given by L = Iωt, where I is the moment of inertia of the wheel and ω is its angular speed. Therefore, the angular momentum of the wheel is L = (4.1 kg)(0.33 m)2(6.0 s-1)(0.10 s) = 0.123 kgm2s-1. E. Gravity cannot cause the axle of the spinning bicycle wheel to tilt downwards (-y direction) because the wheel is spinning, which means that it has an angular momentum. This angular momentum acts as a stabilizing force and prevents the wheel from falling down.

 

[nlightner]

Hello there, it's great that you are taking the time to study for your physics exam. I can understand your frustration with not being able to find help in the busy help room. I will do my best to assist you with this review problem.

A. In this configuration, the most significant forces acting on the gyroscope are the weight (due to gravity), the normal force (from the mounting post), and the force of friction (if any). The vector sum of these forces will be equal to the centripetal force required to keep the gyroscope in its circular path.

B. To find the angular momentum of the wheel, we can use the formula L = Iω, where I is the moment of inertia and ω is the angular velocity. The moment of inertia for a solid disk is 1/2 * MR^2, where M is the mass and R is the radius. We can plug in the given values to find the angular momentum.

C. To find the torque on the gyroscope, we can use the formula τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration. In this case, the angular acceleration is zero, so the torque will be zero as well.

D. To find the angular momentum at a time t = 0.10 s later, we can use the formula L = L0 + τt, where L0 is the initial angular momentum and τ is the torque. We can use the values found in part C to calculate the angular momentum at this time.

E. Gravity can cause the axle of the spinning bicycle wheel to tilt downwards, but it will not cause it to fall down. This is because the spinning wheel has angular momentum, which is conserved. This means that the wheel will continue to spin and maintain its orientation, even if it tilts downwards. In contrast, a non-spinning wheel would fall down due to the force of gravity.

I hope this helps with your review. Best of luck on your exam!