Question

In: Physics

The picture below shows an isolated system with a fairly massive wheel at one end, attached...

The picture below shows an isolated system with a fairly massive wheel at one end, attached via its axle to a long shaft, like a bike tire on a bike frame, but the bike frame is merely a low mass 'truss.' At the other end of this long shaft is a mass of roughly the same magnitude as the wheel, so the center of gravity (CG) is roughly in the middle of the shaft. This mass is fixed to the shaft with no rotation possible. The assembly is floating motionless in 'space', with no contact to anything else.

Diagram of apparatus

If a motor on the 'truss' causes the wheel to spin in one direction, the truss would begin to spin in the other direction about the common center of mass. The net angular momentum would thus be zero both before and after the spinning commences. The wheel and the truss would rotate in the same plane. The actual rotation rate of each part is dependent upon the individual masses, wheel radius, and the length of the shaft. It is getting complex, but so far easy enough to envision in general.

Now, place into the 'truss' a mechanism that causes this long shaft to rotate on its long axis (which would be perpendicular to the spin axis) while it is still undergoing the above rotation relative to the wheel. Upon rotation at this new joint, a force is applied to the axle of the spinning wheel (and of course to the mass at the other end of the truss, too) causing each part to try to turn in the opposite direction. Given that the net angular momentum is still zero, the vector sum of the individual parts (the spinning wheel and the body as a whole rotating around its CG) must be equal and opposite. I cannot envision the result, however, nor do I have the background to derive the equations of motion of this 'whirly gig.' The best I can imagine is that the plane of overall rotation should change, with the plane of the wheel's rotation changing in the opposite direction. This would seem to result in a state where the wheel is no longer spinning in the same plane as the overall assembly, but that would seem unsustainable and perhaps unstable. How can the behavior of this system be understood?

Solutions

Expert Solution

The drawing you generated is much better than my poor attempt, and accurately shows the important aspects of the problem. Thank you. There is one difference, however. My system is literally floating in outer space, with no contact holding it up. This could be approximated in the apparatus you drew by having the support be, say, a ball joint which allows for more freedom of motion of the entire assembly so that it can wobble. Or it could be hung with a u-joint at the c.g.

To set up the problem, it starts with everything motionless. When the motor is started to spin up the disk, the rest of the assembly starts to rotate in the opposite direction to maintain the net angular momentum at zero. The complicated part comes next.

My suspicion is that, once the joint in the horizontal shaft at the blue support is twisted (not continuous spinning, just tilted), thus tipping the spinning disk, the entire length of the shaft will start to wobble as it rotates. This would be in response to the fact that the moment of the spinning disk has tipped, and an equal but opposite tilt in the moment of the spinning assembly must occur for the net angular momentum to remain at 0. As it spins, both these moments will precess, but will continue to cancel each other out. And when the joint at the blue support is returned to the original orientation, this wobbling will stop and the assembly will return to spinning in the original plane. It might make an interesting toy, but that is not what I am aiming for. My goal is to find a way to manipulate the spinning apparatus so that the plane of rotation of the entire assembly can be changed to a different (but stable!) plane. Replacing the rotating joint with a simple 'knee' joint would seem to result in the same behavior. Despite the fact that there is no net angular momentum, the system seems to resist my attempts to 'capture' it in a new orientation.


Related Solutions

5.Consider again the picture you selected in question #3. What’s attached to the 5’ end of...
5.Consider again the picture you selected in question #3. What’s attached to the 5’ end of this molecule? (BOLD the correct answer)    A phosphate group    OR    An OH group (which is attached to the ribose sugar) 6.Consider again the picture you selected in question #3. The way it’s drawn on this page, the bottom end of this molecule is considered to be the…(BOLD the correct answer)             3’ end      OR      5’ end
The picture below shows an incomplete pictorial representation of the situation described in this problem
The picture below shows an incomplete pictorial representation of the situation described in this problem. For symmetry reasons, the coordinate system is chosen so that its origin coincides with the point P at which you want to calculate the magnetic field, and the wire lies in the xy plane. The z axis is perpendicular to the page, pointing out of to the page.As outlined in the strategy above, the wire has been divided into very short segments. For clarity, only...
A ball is attached to one end of a wire, the other end being fastened to...
A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.6 kg and 2.3 kg, and the length of the wire is 1.21 m....
Figure 8-31 shows a ball with mass m ? 0.341 kg attached to the end of...
Figure 8-31 shows a ball with mass m ? 0.341 kg attached to the end of a thin rod with length L ? 0.452 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held horizontally as shown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertically up position, with zero speed...
The figure below shows a Ferris wheel that rotates five times each minute. It carries each...
The figure below shows a Ferris wheel that rotates five times each minute. It carries each car around a circle of diameter 20.0 m.What force (magnitude and direction) does the seat exert on a 53.0-kg child when the rider is halfway between top and bottom? (direction is measured inward from the vertical) I got 588.7365. It is telling me i am within 10% of the correct value but i cant seem to get the right answer. i tried again and...
One end of a horizontal rope is attached to a prong of an electrically driven tuning...
One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at 125 Hz. The other end passes over a pulley and supports a 1.50 kg mass. The linear mass density of the rope is 5.50×10-2 kg/m .a.What is the speed of a transverse wave on the rope?b. What is the wavelength?c. How would your answers to part (A) change if the mass were increased to 3.00 kg?d. How would your answers...
One end of a cord is fixed and a small 0.400-kg object is attached to the...
One end of a cord is fixed and a small 0.400-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.00 m, as shown in the figure below. When θ = 18.0°, the speed of the object is 7.50 m/s. An object is swinging to the right and upward from the end of a cord attached to a horizontal surface. The cord makes an angle θ with the vertical. An...
A 100 kg uniform beam is attached to a vertical wall at one end and is...
A 100 kg uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end. Calculate the magnitude of the vertical component of the force that the wall exerts on the left end of the beam if the angle between the cable and horizontal is θ = 43°. The angle between the horizontal and the beam is 30 degrees.
A 16.3-kg block rests on a horizontal table and is attached to one end of a...
A 16.3-kg block rests on a horizontal table and is attached to one end of a massless, horizontal spring. By pulling horizontally on the other end of the spring, someone causes the block to accelerate uniformly and reach a speed of 5.99 m/s in 1.37 s. In the process, the spring is stretched by 0.180 m. The block is then pulled at a constant speed of 5.99 m/s, during which time the spring is stretched by only 0.0584 m. Find...
A 11.4-kg block rests on a horizontal table and is attached to one end of a...
A 11.4-kg block rests on a horizontal table and is attached to one end of a massless, horizontal spring. By pulling horizontally on the other end of the spring, someone causes the block to accelerate uniformly and reach a speed of 4.08 m/s in 1.13 s. In the process, the spring is stretched by 0.231 m. The block is then pulled at a constant speed of 4.08 m/s, during which time the spring is stretched by only 0.0543 m. Find...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT