They may not notice it, but people living at the equator are moving faster than the speed of sound.
Equations of Rotational Kinematics
In Chapter 2 we defined the kinematic equations for bodies moving at constant acceleration. As
we have seen, there are very clear rotational counterparts for linear displacement, velocity, and
acceleration, so we are able to develop an analogous set of five equations for solving problems in
rotational kinematics:
In these equations, is the object’s initial angular velocity at its initial position,.
Any questions on SAT II Physics that call upon your knowledge of the kinematic equations will
almost certainly be of the translational variety. However, it’s worth noting just how deep the
parallels between translational and rotational kinematics run.
Vector Notation of Rotational Variables
Angular velocity and angular acceleration are vector quantities; the equations above define their
magnitudes but not their directions. Given that objects with angular velocity or acceleration are
moving in a circle, how do we determine the direction of the vector? It may seem strange, but the
direction of the vector for angular velocity or acceleration is actually perpendicular to the plane in
which the object is rotating.
We determine the direction of the angular velocity vector using the right-hand rule. Take your
right hand and curl your fingers along the path of the rotating particle or body. Your thumb then
points in the direction of the angular velocity of the body. Note that the angular velocity is along
the body’s axis of rotation.
The figure below illustrates a top spinning counterclockwise on a table. The right-hand rule shows
that its angular velocity is in the upward direction. Note that if the top were rotating clockwise,
then its angular velocity would be in the downward direction.