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Summary of Sections 8.1, 8.2, and 8.3

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Section 8.1 gives us a good background by defining several important terms. The center of a circular path defines a line called the axis of rotation. The angle that an object rotates about a fixed axis is called the angular displacement (). Counterclockwise displacement is considered positive, and clockwise negative. Angular displacement can be expressed in degrees, revolutions, or radians.
A radian is the measure of the angle subtended by an arc that is the length of the given radius. 2 rad is equal to 360. Therefore, 1 rad is equal to 57.3. Section 8.2 discusses angular velocity . Average angular velocity is derived in a similar way to the average linear velocity we have already discussed. It is simply the angular displacement divided by the elapsed time, and it is usually measured in radians per second. This section also deals with the difference between instantaneous and average angular velocity. This is also analogous to what has already been discussed with linear velocity. Also similar to the concepts we have already dealt with in linear motion is the concept of angular acceleration (), which is simply a change in the angular velocity. Section 8.3 clarifies the equations (similar to those used in linear motion study) that are necessary to work problems dealing with angular motion. These are the equations of rotational kinematics for constant angular acceleration:
 = 0 + t
 = ½ (0 + )t
 = 0t + ½ t2
2 = 02 + 2
Also in this section is a useful table of symbols:

Quantity Rotational Motion Linear Motion
Displacement  X
Initial Velocity 0 v0
Final Velocity  V
Acceleration  A
Time t T

This section closes with a list of reasoning strategies for applying these equations.
1. Make a drawing
2. Decide on a positive and negative direction
3. Write down values for the variables
4. Make sure you have values

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