The Basics
Chapter 3 - Understanding motion
Section 3.4 - Rotational motion
There are two ways an object can move. One is by translation and the
other is by rotation. Translation basically means an object moves in a
straight line in the same direction. Rotation, on the other hand, is when
an object can pivot about a stationary point. The equations of motion to
describe translation are quite straightforward. It is basically F = ma,
where the objects acceleration is simply the force divided by its mass.
But how do we describe rotation? An object can rotate about any fixed
point. While forces give rise to translation, it is couples that create
rotation. A couple is two equal but opposite
forces applied a perpendicular distance from each other. For example, consider
the airplane propeller shown below:
A couple is created by applying a force in one direction at the top of
the propeller and an equal but opposite force in the other direction at the
bottom of the propeller. As long as the forces are applied perpendicular to
the point of rotation then it will cause the propeller to start rotating.
The magnitude of the couple is the force multiplied by the distance
between the two forces. This value determines the rotational acceleration
of the propeller.
The obvious question then is what happens if we only apply force on
one end of the propeller? What kind of rotational acceleration will that
give rise to? To answer this we have to interpret this force in terms of
its translational component and its rotational component defined by a
couple. So the same force on the other can be expressed the following way:
The two force diagrams are statically equivalent. This means they both
cause the object to move in exactly the same way. This is fundamentally
important because it lets one define any force in terms of its
translational force component and rotational couple component.
Why did we express the force couple as only one half the original
force? I will explain this later as this chapter is a work in progress.
Send me a note using the form below if you'd like to see more details on
this subject.
