Lecture 3: rigid body dynamics
               kinematics example: rolling no slip
            •
               rotational equation of motion
            •
               mass moment of inertia
            •
               solving rigid body dynamics problems
            •
               dynamics example: pulley with mass
            •
 Thursday, April 11, 13
            Rigid Body Kinematics
         v =v +(!⇥r                        )
           A        B                A/B
         a =a +(↵⇥r                        )+(!⇥(!⇥r                     ))
           A        B                A/B                          A/B
 • Useful Shortcuts for 2D planar motion ↵ = ↵k
                                                              ! =!k
                                                              r = rxi +ryj
                    !⇥r=ry!i+rx!j
                      ↵⇥r=ry↵i+rx↵j
          !⇥(!⇥r)=r !2ir !2j
                                          x               y
 Thursday, April 11, 13
             Rigid Body Dynamics
    Linear Motion:                                 sum of the forces is the 
             F=ma=d(mv)                            time rate of change of 
                               dt                  linear momentum
    Works for particles - and also works for rigid bodies if 
    the acceleration is at the center of mass!
                              F=maG
 Thursday, April 11, 13
             Rigid Body Dynamics
    Rotational Motion:
                        d(HG)            ˙         sum of the moments is 
            M =                     =H
                G           dt            G        the time rate of change 
                                                   of angular momentum
                about the center of mass
 Thursday, April 11, 13