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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 Velocity.

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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

Instantaneous Center of Zero Velocity

Relative Acceleration

Relative-Motion Analysis :


Examples of Non-Relative-Motions

)sliding connections and has two independent motion)


Position

Rotating axes

Position


Velocity
Velocity

Rotating axes & translating object

wr + v


Velocity1
Velocity

  • VC = Velocity of the Collar, measured from

  • the X, Y, Z reference

  • VO = Velocity of the origin O of the x,y,z reference

  • measured from the X,Y,Z reference

  • (VC/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

    rC/O = relative position of “C with respect to O”


Acceleration
Acceleration

Acceleration is the time derivative of velocity

Rotating axes & translating object

(wr + v)


Acceleration of origin

Acceleration of the object

a r

Tangential acceleration

w2 r

Normal acceleration

Coriolis acceleration

Rotating axes & translating object

(wr + v)


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

Rearrange

Compare !


Recall – Cylindrical coordinate

Coriolis acceleration


Example 16-20

aC/D = ?

wDE = ?

aDE= ?



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