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lecture+notes+20 - 14:440:222 Dynamics (Lecture Note #20)...

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14:440:222 Dynamics (Lecture Note #20) Instructor: Prof. Peng Song Rutgers University
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Today’s Lecture • Planar kinetics of rigid body: Translational and fixed-axis rotational motion
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The boat and trailer undergo rectilinear motion. In order to find the reactions at the trailer wheels and the acceleration of the boat, we need to draw the FBD and kinetic diagram for the boat and trailer. How many equations of motion do we need to solve this problem? What are they? Applications
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The pendulum of the Charpy impact machine is released from rest when θ = 0°. Its angular velocity ( ω ) begins to increase. Can we determine the angular velocity when it is in vertical position ? On which property (P) of the pendulum does the angular acceleration ( α ) depend ? What is the relationship between P and α ? Applications (cont’d)
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We will limit our study of planar kinetics to rigid bodies that are symmetric with respect to a fixed reference plane. As discussed in Chapter 16, when a body is subjected to general plane motion, it undergoes a combination of translation and rotation. First, a coordinate system with its origin at an arbitrary point P is established. The x-y axes should not rotate and can either be fixed or translate with constant velocity. Planar Kinetic Equations of Motion
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• If a body undergoes translational motion, the equation of motion is Σ F =m a G . This can also be written in scalar form as Σ F x = m(a G ) x and Σ F y = m(a G ) y In words: the sum of all the external forces acting on the body is equal to the body’s mass times the acceleration of it’s mass center. Equations of Translational Motion
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an external force system. The moment about point P can be written as: Σ ( r i × F i ) + Σ M i = r × m a G + I G α Σ M p = Σ ( M k ) p where r = x i + y j and Σ M p is the resultant moment about P due to all the external forces. The term
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lecture+notes+20 - 14:440:222 Dynamics (Lecture Note #20)...

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