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picture1_Rotational Dynamics Pdf 158244 | Emech Equilibrium Review V1


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File: Rotational Dynamics Pdf 158244 | Emech Equilibrium Review V1
engineers mechanics introduction definitions assumptions mechanics statics body at rest under action of forces all quantities time independent dynamics body in motion under action of forces all quantities time dependent ...

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                            Engineers Mechanics- Introduction
                               Definitions, assumptions
                                   • Mechanics:
                                                     -       Statics – body at rest under action of forces. All quantities time 
                                                             independent
                                                     -       Dynamics–body in motion under action of forces. All quantities 
                                                             time dependent
                                     • Rigid Body Mechanics:
                                                     Assume rigid body– no deformation, original geometry
                                      A ‘particle’ idealizes a body by placing its mass at its center and neglecting its 
                                      dimensions.
                                   ©©  IIT IIT Bombay Bombay ,,  CE CE Dept,Dept,  Lecture Lecture Notes Notes for for CE201 CE201                                                                                                                 1 - 1
        Engineers Mechanics-Equilibrium of Rigid Bodies
        Introduction
             • For a rigid body in static equilibrium, external forces and moments 
               are balanced and will impart no translational or rotational motion 
               to body.
             • Condition for static equilibrium of a body is that resultant force and 
               resultant couple due to all external forces are zero,
                                           
                                         
                  R0;         M  rF0
                            O 
             • Resolving into rectangular Cartesian components leads to 6 scalar 
               equations for static equilibrium,
                    F 0       F 0        F 0
                  x          y          z
                   M 0        M 0        M 0
                  x          y          z
          © IIT Bombay , CE Dept, Lecture Notes for CE201       1 - 2
        Engineers Mechanics-Equilibrium of Rigid Bodies
        Free-Body Diagram (Most Important Step)
                                 Show all forces acting on the body in a free-body
                                 diagram.
                                  • Select entire body, isolate it from ground and 
                                   from other bodies.
                                 • Show applied external forces/moments (magn. 
                                   & dir.) at their points of application (include 
                                   self weight of body).
                                 • Show unknown forces/moments (with assumed 
                                   direction) at their points of application. These 
                                   usually consist of reactions by which the 
                                   ground and other bodies oppose the possible 
                                   motion of the body.
                                 • Show dimensions necessary to compute 
                                   moments due to forces.
          © IIT Bombay , CE Dept, Lecture Notes for CE201       1 - 3
                              Engineers Mechanics-Equilibrium of Rigid Bodies
                               Reactions from supports and connections
                                      Supports and connections hold body in position (equilibrium) under action 
                                      of externally applied forces 
                                        Body exerts force on support / connection. From Newton’s third law, 
                                        support / connection exerts equal and opposite reaction force on body 
                                        The reaction force on body opposes the motion of the body. 
                                          For a 2D body,  2 translational motions and 1 rotational motion possible
                                          For a 3D body,  3 translational motions and 3 rotational motions possible
                                   ©©  IIT IIT Bombay Bombay ,,  CE CE Dept,Dept,  Lecture Lecture Notes Notes for for CE201 CE201                                                                                                                 1 - 4
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...Engineers mechanics introduction definitions assumptions statics body at rest under action of forces all quantities time independent dynamics in motion dependent rigid assume no deformation original geometry a particle idealizes by placing its mass center and neglecting dimensions iit bombay ce dept lecture notes for equilibrium bodies static external moments are balanced will impart translational or rotational to condition is that resultant force couple due zero r m rf o resolving into rectangular cartesian components leads scalar equations f x y z free diagram most important step show acting on the select entire isolate it from ground other applied magn dir their points application include self weight unknown with assumed direction these usually consist reactions which oppose possible necessary compute supports connections hold position externally exerts support connection newton s third law equal opposite reaction opposes d motions...

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