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RotationalKinematics - Rotational Kinematics We have talked...

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Rotational Kinematics We have talked about how our position vectors can be represented as groups of numbers, for instance either in individual components or as the magnitude and angles associated with the vector. Then, in introducing centripetal motion, we saw that the acceleration is what causes the object to curve into the circular shape. Later we will see that the equivalent force associated with centripetal motion is not a "physical" force, so in many ways we would like to introduce a new notation in which we no longer have to consider centripetal motion. This is done by considering rotational motion. Rotational motion concerns the motion of an object about some central point associated with the object. We shall see that all of the mechanical relationships that we have found so far have equivalents in rotational motion. Angular Displacement To begin, let us consider the rotation of a ball around its center. How far does a point on the surface move? From geometry, we know that if the ball rotates through an angle θ , then the surface will move a distance x = r θ . This lets us write θ = x r (4.1) Notice that both x and r are distances, so that θ is dimensionless. We associate
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