Lecture 5-6C: Gyroscopic Motion

Conservation of Angular Momentum

In the absence of any external torques on a system:

Angular momentum conservation preserves both the spinning rate AND the orientation of an object

Gyroscope for the International Space Station Credit: NASA https://en.wikipedia.org/wiki/Control_moment_gyroscope#/media/File:ISS_gyroscope.jpg

The Earth is a spinning body Credit: NASA https://commons.wikimedia.org/wiki/File:1_Earth_(blank_2).png

Bicycle wheels have angular momentum Credit: Andy Armstrong: https://en.wikipedia.org/wiki/Mountain_biking#/media/File:Mountain-biker-climbs.jpg

Spinning top by Dhor https://upload.wikimedia.org/wikipedia/commons/5/57/Snurra_uppochner.gif

Some really fun toys!

Gyroscope animation from giphy.com: http://giphy.com/gifs/gyroscope-F62lPOGDf5XzO

Some really fun toys!

Accelerations change direction of motion

x

y Constant circular motion requires a centripetal acceleration to change the velocity direction

Mg

T

1

2

rotation

3 (initially)

Model of a gyroscope wheel

⇒ result is pendulum motion

R M

Mg

T

rotation

Model of a gyroscope wheel

R M

View from above

View from above

View from above

Gyroscope animation from giphy.com: http://giphy.com/gifs/gyroscope-F62lPOGDf5XzO

The precessional motion of gyroscope is the reorientation of the angular momentum vector by

gravitational torque

Precession of the Earth

The Earth's rotational axis points toward the North star, but its orientation precesses every 26,000 years

The North star won't always be due North!

Credit: Kevin Hadley https://en.wikipedia.org/wiki/Celestial_pole#/media/File:Star_Trails_Shoreline.jpg

The angular momentum of a spinning object points toward its orientation; an applied torque can change that orientation

Gyroscopic motion is the rotational equivalent of circular translational motion - a rotational orbit

Many spinning objects, including the Earth precession and change orientation due to external torques

Summary