30 π/6
45 π/4
60 π/3
90 π/2
180 π
360 2π
Calculating the Length of an Arc
The advantage of using radians instead of degrees, as will quickly become apparent, is that the
radian is based on the nature of angles and circles themselves, rather than on the arbitrary fact of
how long it takes our Earth to circle the sun.
For example, calculating the length of any arc in a circle is much easier with radians than with
degrees. We know that the circumference of a circle is given by P = 2 πr, and we know that there
are 2π radians in a circle. If we wanted to know the length, l, of the arc described by any angle ,
we would know that this arc is a fraction of the perimeter, ( /2π)P. Because P = 2 rπ, the length of
the arc would be:
Rotational Kinematics
You are now going to fall in love with the word angular. You’ll find that for every term in
kinematics that you’re familiar with, there’s an “angular” counterpart: angular displacement,
angular velocity, angular acceleration, etc. And you’ll find that, “angular” aside, very little
changes when dealing with rotational kinematics.
Angular Position, Displacement, Velocity, and Acceleration
SAT II Physics is unlikely to have any questions that simply ask you to calculate the angular
position, displacement, velocity, or acceleration of a rotating body. However, these concepts form
the basis of rotational mechanics, and the questions you will encounter on SAT II Physics will
certainly be easier if you’re familiar with these fundamentals.
Angular Position
By convention, we measure angles in a circle in a counterclockwise direction from the positive x-
axis. The angular position of a particle is the angle, , made between the line connecting that
particle to the origin, O, and the positive x-axis, measured counterclockwise. Let’s take the
example of a point P on a rotating wheel: