# King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 25.

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King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 25

General Plane Motion Position Velocity Acceleration

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

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

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

Rolling wheel with-out slipping G a t =0

Example 16-13

Example 16-15 a A =? a B =?

Example 16-16

Example 16-17

Example 16-18