If we have a rotating object, we say that it has what we call “angular momentum.”
We can represent the angular momentum with an arrow.
The direction of the arrow indicates the axis of rotation.
The length of the arrow represents the strength of the angular momentum.
If we apply forces to increase or decrease the rotation,
we say that we are applying a torque on the object.
The torque can also be represented with an arrow.
The direction of the arrow indicates
the axis around which the torque is trying to rotate the object.
The length of the arrow indicates the strength of the torque.
The arrow for the torque indicates
how quickly the arrow for the angular momentum is changing with time.
But, what if we apply a force causing the object to rotate
in a different direction than the one in which the object is already rotating?
The torque arrow will be along the axis that the force is trying to rotate the object.
The angular momentum arrow will change
based on the direction in which the torque arrow is pointing.
This means that after will the torque is applied,
the new angular momentum arrow will now be pointed in this direction.
The angular momentum arrow always indicates the axis around which the object is rotating.
This means that as a force is applied, the rotation of the object changes as is shown.
To understand why this is happening, consider a ring rotating in space.
Suppose we apply a force to this ring.
Each point on the ring will want to continue moving in the same direction as before.
These two points will cause the object to move like this.
And these two other points will cause the object to move like this.
The events shown here all happen at the same time, and this is the result.
This means that when we apply a force to a rotating object,
its rotation is changed to look like this.
This creates the illusion that the force was really applied
90 degrees ahead in the rotation.
This is the behavior that is described by the arrows
for torque and angular momentum as was shown.
The force of gravity will create a torque on an object.
The arrow representing this torque will be
pointed along the axis around which gravity is trying to rotate the object.
The angular momentum arrow will change
based on the direction in which the torque arrow is pointing.
As a result, the spinning object will react to the force of gravity as shown.
The faster an object is spinning, the greater its angular momentum,
and the longer the angular momentum arrow.
If the angular momentum arrow is very long, then the addition of
the torque arrow will have very little impact on the overall direction of the arrow.
This means that if the object is spinning very rapidly, the applied torque
will have very little impact on the object’s direction of rotation.
This is the basic principle of a gyroscope,
which are critical in the navigation of aircraft and spacecraft.
A gyroscope has a disk that spins very rapidly.
This means that applied torques to the disk will have
little effect on the disk’s direction.
As the vehicle inside which the gyroscope is located rotates,
the spinning disk will tend to stay oriented in the same direction in space.
When a gyroscope is placed inside an aircraft or spacecraft, measuring the orientation
of the gyroscope allows us to determine what direction the vehicle is pointed in.
Much more information about the laws of motion
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