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Learn how to analyze absolute motion of bodies, understand translation and rotation, and calculate velocities and accelerations. Practice examples included.
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Absolute Motion Analysis • A body subjected to general plane motion undergoes simultaneous translation and rotation. • The motion can be completely describe by knowing • Angular rotation of a line in the body • The motion of a point on the body.
Absolute Motion Analysis • We define these motions by • using the rectilinear coordinate s to locate a position along its path. • using the angular position coordinate θ to specify the orientation of the line. • The two coordinates (s and θ) are then related using the geometry of the problem. • Linear velocity and angular velocity are related by taking time derivates and applying the chain rule.
Lecture Example 1: The bar remains in contact with the floor and with Point A. If Point B moves to the right with a constant velocity vB, determine the angular velocity and the angular acceleration of the bar as a function of x.
Lecture Example 2: The bar is confined to move along the vertical and inclined planes. If the velocity of the roller at A 6 ft/s when θ=45°, determine the bar’s angular velocity and the velocity of the roller B at this instant.
