Cracking the SAT Physics Subject Test

If the disk rotates as a rigid body, then all three dots shown have the same angular
displacement, ∆θ. In fact, this is the definition of a rigid body: In a rigid body, all
points along a radial line always have the same angular displacement.

Just as the time rate-of-change of displacement gives velocity, the time rate-of-
change of angular displacement gives angular velocity, symbolized by ω (omega).

The definition of the average angular velocity is

Finally, just as the time rate-of-change of velocity gives acceleration, the time rate-
of-change of angular velocity gives angular acceleration, or α (alpha).

The definition of the average angular acceleration is

On the rotating disk illustrated on the previous page, we said that all points undergo
the same angular displacement at any given time interval; this means that all points
on the disk have the same angular velocity, ω, but not all points have the same
linear velocity, v. This follows from the definition of radian measure. Expressed in
radians, the angular displacement, ∆θ, is related to the arc length, ∆s, by the
equation

Math Brush Up: Radians

The radian is the standard

unit of angular measure.

It is the measurement of

the angle that describes

a length of the the unit

circle. For instance, one

radian, π, is 180º, or half of

a circle. A full circle is 2π.

Rearranging this equation and dividing by ∆t, we find that