Relation between linear and angular variables

Relation between linear and angular variables - The...

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Relation between linear and angular variables An example of the relation between angular and linear variables has already been discussed. Figure 1 illustrates how the distance s, covered by point A, is related to the radius of the circle and the angle of rotation The velocity of point A can be obtained by differentiating this equation with respect to time To derive this equation we have assumed that for rotations around a fixed axis the distance r from point A to the rotation axis is constant (independent of time) which is true for a rigid body. The acceleration of point A can be determined as follows The acceleration a t is the tangential component of the linear acceleration, related to the change in the magnitude of the velocity of point A. However, we have seen that an object carrying out a circular motion also experiences a radial acceleration
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Unformatted text preview: . The magnitude of the radial component, a r , is Using the previously derived expression for v in terms of [omega] and r, we can rewrite the radial component of the acceleration as follows Figure 11.2 shows the direction of both the radial and the tangential components of the acceleration of point A. The radial component is always present as long as [omega] is not equal to zero; the tangential component is only present if the angular acceleration is not zero. Figure 11.2. Components of the acceleration of point A. We can conclude that when a rigid body is rotating around a fixed axis, every part of the body has the same angular velocity [omega] and the same angular acceleration a, but points that are located at different distances from the rotation axis have different linear velocities and different linear accelerations....
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This document was uploaded on 11/25/2011.

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