Rotational
Kinematics
A common
motion that deserves our attention is that of a object that stays
in place but spins on an axis. Whereas in an earlier section
of this course we dealt with linear motion in a straight line
(this is called translational motion), now we deal with rotational
motion (a.k.a. angular motion).
For a disk rotating at a uniform rate about its axis, every point
on the disk has the same angular displacement theta that
is, each point moves through the same angle. The unit of angle
for this section is the radian.
Note
that 1 revolution =
2 p radians = 6.28 rad.
If we measure the time it takes
to move through an angle, we can determine the angular velocity
w (symbol
is w omega),
measured in rad/s. Again, if the angular velocity of an object
changes during some amount of time, we can determine the angular
acceleration a measured in rad/s/s (a symbol is alpha).
Of particular interest to us is the relationship between the
angular velocity of a rotating object and the linear velocity
of point on its surface. Consider the Earth. Every point on the
planet rotates through 2 p radians in 24 hours, about a quarter of a radian/hr.
Not every point on the surface has the same linear velocity.
The relationship between them is v = (r) (w). Hence, the further out from the center of rotation
is some point, the larger is its linear velocity. Can you determine
the linear velocity of some point on the equator? What is the
linear velocity for Waterville (latitude 44.5 degrees)?
Visit these web sites for additional
explanation of this topic.
http://www.mcasco.com/p1rot.html
The statements
at the immediate right address the determination of the magnitude
of angular displacement, angular veloccity and angular axxeleration.
At far right are equations that are to rotary motion what page
1 equations are to motion j n one dimension






For a first view of what causes things
to rotate the way they do, see
http://www.mcasco.com/p1rdy.html
Go tp problems at U Oregon
http://www.zebu.uoregon.edu/~probs/mech/circ.html
Return
to mechanics
This page last edited 01/23/09. 