Angular Momentum Conservation of Angular Momentum With Brief Description of a Gyroscope Physics 109, Fall 2017 Experiment Number 11 in the Physics 109 Lab Manual (page 50)
Gyroscope Precession
Outline Quiz Results History of the Gyroscope Foucault Pendulum Description of the Experiment Class Questions
Quiz Results There were 19 participants Three had correct answers for both instances of the question Five had one correct answer Next an explanation of the gyroscope
History First discovered in 1817 by Johann Bohnenberger Actual invention and name attributed to Leon Foucault in 1852 He was trying to measure the rotation of the Earth Friction limited trials to 8-10 minutes, not long enough Foucault noted for something else to be described later...
Why does a gyroscope not fall down? We now have a situation in which the angular momentum vector is perpendicular to a torque vector. The torque arises from change in the angular momentum vector... its direction not its magnitude. As a result, the gyroscope PRECESSES and does not fall down.
Important relations The angular speed of precession, W, is given by the ratio of the torque divided by the angular momentum. The torque arises from the force of gravity on the spinning gyroscope, times the length of the lever arm...mgd = t This applies assuming that the rotational speed of the gyroscope is much higher than the precession rate.
Precession s,ls d mg
Key to Understanding: Finding the directions in which angular momentum is conserved.
Precession Diagram from the text: Gravity exerts torque t is into the page by the right hand rule Since torque is horizontal, the change in DL is horizontal
Precession (continued) Thus, the gyroscope does not fall down... Instead, it PRECESSES, in this case, in a counterclockwise direction. (viewed from above) (Note that the disk is spinning counterclockwise and L thus points out along the axis)
More History First marine gyroscopes developed between 1905 and 1908 in Germany. In 1910 American Elmer Sperry developed his own design. Shortly thereafter the Sperry Gyroscope Company was providing aircraft and ships with gyroscope stabilizers. Today, the Hubble Space Telescope uses gyroscopes for stabilization.
Space Telescope and a Photo
Antenna boom (there are two)
Antenna Boom Design Aluminum-graphite metal matrix composite (graphite fibers embedded in a 6061 aluminum alloy matrix) Wires made by drawing a graphite fiber tow through molten aluminum alloy
Why this approach? Aluminum stiffness-10, graphite stiffness-70 Aluminum thermal expansion-- 22 Graphite thermal expansion-- -9 So thermal/mechanical stability is outstanding Structural component can also serve as the waveguide Saved about 60% of the original design weight
Foucault Pendulum Plane of swing remains fixed while the earth rotates. Returns to original orientation in two days.
YouTube movies http://www.youtube.com/watch?v=amxlvduf4vy&feature=related http://www.youtube.com/watch?v=xjc1dnbvk_0
Description of the Experiment There are three parts to the experiment Orbiting puck Changing Moment of Inertia Changing orientation of a spinning bicycle wheel. Background Angular momentum is also a conservation law L M r v Where r X v is a vector cross product, so L is perpendicular to the r-v plane, and the right hand rule applies.
Description of the Experiment (2) Also: L r mv r p The magnitude of L is mrvp where vp is the component of velocity perpendicular to r. For extended objects, L = I Where I is the moment of inertia and is the angular velocity. L and point in the same direction.
More Angular Momentum As with linear momentum, angular momentum is conserved at the component level. L Lx, L y, Lz If an external force is applied to change only Lx, Ly and Lz remain unchanged. As with linear momentum, conservation of angular momentum does not require conservation of energy.
Orbiting Puck Attach puck to a post in the center of the table using a lightweight spring. The spring constant does not have to be measured. Practice sending the puck on an elliptical orbit. Record path using 20 Hz spark, more than one revolution to record decay due to energy loss. Measure r (max) and r (min) Measure distance between sparks at these points to obtain velocities.
Changing Moment of Inertia Stand or sit on a rotatable platform with your arms close to your sides. (hold weights) Have your lab partner spin you around at a moderate rate Raise your arms to horizontal and record your observations. (Experience the figure skater s spin without having to jump!)
Spinning Bicycle Wheel Spin the bicycle wheel by hand Orient the wheel so the axle is horizontal, and the top of the wheel is going away from you. Step onto the rotating platform. Next, reorient the axle so that it is pointing downward 45 degrees to the left. Next, reorient the axle so that it is pointing upward 45 degrees to the left. (It may be necessary to step off the platform to re-spin the wheel.)
Spinning Bicycle Wheel (2) Step off the platform, re-spin the wheel, and orient the axle ( or L) to point directly up, then step onto the platform. Reorient or L to point 45 deg. to your left, then right. Then do the same for 45 deg. front and back. Finally, return or L to point straight up and stop the wheel rotation with your hand. Record observations. Step off platform, re-spin wheel, point up, step on platform, then flip or L 180 degrees, and record observations.
What is the torque on the bolt? r F A. r dot F D. r - F B. r cross F C. r + F
A Merry-Go-Round Problem A boy jumps on the MGR moving toward the center, stopping at the rim. What happens? A. Nothing, the MGR speed stays the same B. MGR slows down C. MGR speeds up D. MGR stops
Second MGR Problem Girl running in the same direction as the MGR is rotating jumps on. What happens? A. Nothing B. MGR slows down C. MGR speeds up D. MGR stops
Bicycle Wheel Problem--1 With wheel axle horizontal, and the wheel top rim going away, which direction does L or point? A. Right B. Left C. Up D. Down
Bicycle Wheel Problem--2 After stepping on rotatable platform, left end of axle is tilted down 45 degrees. What happens? A. Nothing B. Platform rotates right C. Platform rotates left D. None of the above
Bicycle Wheel Problem--3 Now the left end of the axle is tilted up 45 degrees. What happens? A. Nothing B. Platform rotates right C. Platform rotates left D. None of the above
Bicycle Wheel Problem--4 Standing on the platform, axle and L or point straight up. Now tilt axle 45 degrees to the right. What happens? A. Nothing B. Platform rotates right C. Platform rotates left D. Not enough information Does it matter which direction the axle is tilted?
Bicycle Wheel Problem--5 With the axle (and L) pointing straight up, stop the wheel quickly. What happens? A. Nothing B. Platform rotates right C. Platform rotates left D. Not enough information
Bicycle Wheel Problem--6 With axle and L pointing straight up, step on platform. Now rotate axle so that it points straight down. What happens? A. Nothing B. Platform rotates right C. Platform rotates left D. Not enough information
Bicycle Wheel Problem--7 If the wheel does not slow down in the previous operation, you now have some added rotational energy. Where does it come from? A. Gravitational potential energy B. Work done in flipping the wheel C. Both of the above D. None of the above