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This causes us to seek a more comprehensive description that will encompass the motion of all of the points on the wheel. Two terms that accomplish that purposeare angular displacement and angular velocity.
Approaching the situation from this viewpoint, we concentrate on angles instead of distances. If a wheel spins through one-fourth of a complete revolution, every point on the wheelmoves through the same 90-degree angle. (However, as you learned in earlier modules, points at different radii move different distances.)
A set of new variables
We will define a set of variables involving angular motion that are analogous to displacement, velocity, and acceleration in the realm of linear motion. However, we will use angular measurements instead oflinear distance measurements.
Angular displacement
Instead of linear displacement, for example, we will speak of angular displacement. Angular displacement is the angle through which a rotating body turns based on some starting and stopping criteria.
A pie-shaped wedge
As you learned in an earlier module, a point on a wheel moves along the circumference of a circle as the wheel rotates. Viewing the rotating wheelfrom a vantage point that is perpendicular to the wheel, during a given time interval, we see that the point sweeps out a pie-shaped wedge with its point at the center of the wheel.
An arc of a circle
The motion of the point describes an arc of a circle directly opposite the point at the center of the circle. This pie-shapedwedge describes an angle, which is the angular displacement during that episode of movement. (You should be able to simulate this on yourgraph board in order to get a better picture in your mind.)
Definition of angular displacement
dA = Af - Ai
where
Physics books typically use Greek letters such as phi and theta to represent angles. However, it is unlikely that your Brailledisplay can handle Greek characters, so I will stick with standard qwerty keyboard characters.
Angular displacement is a signed quantity
The direction of rotation is indicated by the algebraic sign of the angular displacement. It is conventional to consider a counter clockwiserotation to result in a positive angular displacement.
Units of angular displacement
The units of angular displacement are typically degrees or radians.
That brings us to angular velocity, The average angular velocity is the average rate of change of angular displacement.
Definition of angular velocity
wAvg = dA/dT
where
It is customary in physics books to represent angular velocity with the Greek letter omega. In this module, I will use a lower-case"w" character to represent angular velocity where appropriate, simply because it looks a lot like a Greek omega character.
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