concept of center of mass in the previous chapter’s discussion of linear momentum. The concept
of center of mass will play an even more central role in this chapter, as rotational motion is
essentially defined as the rotation of a body about its center of mass.
Axis of Rotation
The rotational motion of a rigid body occurs when every point in the body moves in a circular path
around a line called the axis of rotation, which cuts through the center of mass. One familiar
example of rotational motion is that of a spinning wheel. In the figure at right, we see a wheel
rotating counterclockwise around an axis labeled O that is perpendicular to the page.
As the wheel rotates, every point in the rigid body makes a circle around the axis of rotation, O.
Radians
We’re all very used to measuring angles in degrees, and know perfectly well that there are 360º in
a circle, 90 º in a right angle, and so on. You’ve probably noticed that 360 is also a convenient
number because so many other numbers divide into it. However, this is a totally arbitrary system
that has its origins in the Ancient Egyptian calendar which was based on a 360 -day year.
It makes far more mathematical sense to measure angles in radians (rad). If we were to measure
the arc of a circle that has the same length as the radius of that circle, then one radian would be the
angle made by two radii drawn to either end of the arc.
Converting between Degrees and Radians
It is unlikely that SAT II Physics will specifically ask you to convert between degrees and radians,
but it will save you time and headaches if you can make this conversion quickly and easily. Just
remember this formula:
You’ll quickly get used to working in radians, but below is a conversion table for the more
commonly occurring angles.
Value in degrees Value in radians