King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 28

Examples of relative motions “ motion of one part lead to the motion of other parts ” (pin-connected rigid body)

Relative-Motion Analysis : Relative Velocity Relative Acceleration Instantaneous Center of Zero Velocity

Examples of Non-Relative-Motions )sliding connections and has two independent motion)

Position Rotating axes

Velocity Rotating axes & translating object  r + v

Velocity V C = Velocity of the Collar, measured from the X, Y, Z reference V O = Velocity of the origin O of the x,y,z reference measured from the X,Y,Z reference (V C/O ) xyz = relative velocity of “ C with respect to O ” observer attached to the rotating x,y,z reference  = angular velocity of the x,y,z reference, measured from the X,Y,Z reference r C/O = relative position of “ C with respect to O ”

Acceleration Acceleration is the time derivative of velocity Rotating axes & translating object  r + v)

Rotating axes & translating object  r + v)  r Tangential acceleration  2 r Normal acceleration Coriolis acceleration Acceleration of the object Acceleration of origin

Coriolis acceleration Whenever a point is moving on a path and the path is rotating, there is an extra component of the acceleration due to coupling between the motion of the point on the path and the rotation of the path. This component is called Coriolis acceleration. First measured by the French engineer G.C. Coriolis Important in studying the effect “ force and acceleration ” of earth rotation on the rockets and long-range projectiles

Recall cylindrical coordinate Compare ! Rearrange

Recall – Cylindrical coordinate Coriolis acceleration

Example 16-20a C/D = ?  DE = ?  DE = ?