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King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 25
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General Plane Motion Position Velocity Acceleration
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Recall the relationship for the relation velocities we learned earlier, We can take derivative with respect to time to get : This equation may be explained using the figures below : TranslationRotation
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a B = acceleration of point B a A = acceleration of the base point A = angular acceleration of the body = angular velocity of the body r B/A = relative-position vector drawn from A to B Relative-Acceleration equation
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Procedure for Analysis 1.Establish the direction of x and y 2.Indicate the direction of a A, a B, , and r B/A 3.Apply a B = a A + x r B/A - 2 r B/A in a vector form 4.Evaluate the cross product 5.Equate the respective i and j components to obtain two scalar equation 6.Solve for and a B i j k + x y
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Rolling wheel with-out slipping G a t =0
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Example 16-13
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Example 16-15 a A =? a B =?
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Example 16-16
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Example 16-17
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Example 16-18
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