1. What is precession? this is a powerpoint presentation explaining what precession is and how it happens

2. rotation of two masses connected by a spring ● two masses are connected by a spring and set rotating about their C.M. ● the masses will continue rotating that way forever ● they will be kept in circular motion by the centrifugal force of the spring.

3. Rotation of a Thin Plate ● a thin plate is set in motion rotating about its bottom edge ● the angular velocity is in the y direction

4. rotation of a thin plate ● If the plate in the previous slide is set rotating about its lower edge with the angular velocity in the y direction, it will not keep rotating that way. ● The plate will start to wobble and this wobbling is called precession.

5. Is it possible for the plate to rotate and not precess? ● Imagine the plate is rotated about a diagonal

6. Every object can be rotated such that it does not precess ● You can probably see from the previous picture that if the plate is rotated about its diagonal, it will not precess. ● Think of every point on the plate as a mass with a “mirror” mass on the opposite side of the diagonal. ● Each mass pair will put a centrifugal force on themselves.

7. and object is made up of an infinite number of springs and masses ● imaging putting two sets of springs and masses on top of each other ● now both of these sets of masses together will rotate in a circle. ● now look back at slide 5

8. What is a principle axis? ● A principle axis is an axis (through the C.O.M.) of an object that the object can be rotated about and not precess ● Every object has at least 3 principle axis ● Some objects (ex. sphere) and and infinite number of principle axis ● One principle axis of a plate is its diagonal

9. What if an object does not rotate about a principle axis? ● If and object does not rotate about a principle axis, then that object will precess. ● Precession is when the object wobbles even though no torque is applied to the object. ● To see precession, take a tennis racket and throw it up in the air spinning about the three axis (one at a time) going through its center. It will precess when rotated about one them.

10. Why does precession happen? ● Imagine two masses connected by a stiff rod ● here z is up, y is right left and x is in and out of the page. ● Imagine the angular velocity is some ● amount in the x direction and some in the z ● w=Wx + Wz

11. How will the rod and masses rotate? ● After a short amount of time, the rod on the previous page will look as follows ● It remains in the zy-plane, but it is rotated with an angle to the z axis

12. The moment of inertia of the rod about a fixed axis has changed ● Initially, the moment of inertia of the rod was 2mr^2 in the x-direction and a very very small number in the y-direction. ● After a small time, the moment of inertia of the rod is still 2mr^2 in the x-direction, but not so small in the y-direction. (Each mass has a larger perpendicular distance from the z- axis.)

13. So what does this mean? ● The moment of inertia of the rod about a fixed coordinate system has changed. ● There is no torque acting on the rod so the angular momentum of the rod can't change. ● Angular momentum is equal to (moment of inertia)* (angular velocity) ● If the moment of inertia changes and the angular momentum remains the same then the angular velocity of the rod must change as well. THIS IS WHAT IS KNOWN AS PRECESSION!

14. PRECESSION ● If and object is not rotating about one of its principle axis, its angular velocity will be changing with time even though no torque will be applied to the object. This happens because the moment of inertia of the object will be changing with time as well (relative to a fixed coordinate system).