What is precession?
this is a powerpoint presentation explaining
what precession is and how it happens
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.
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
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.
Is it possible for the plate to
rotate and not precess?
●
Imagine the plate is rotated about a diagonal
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.
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
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
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.
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
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
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 zaxis.)
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
●
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).