MER212: Chapter 17 Kinetics of Rigid Bodiesminerva.union.edu/bucinelr/mer212/LectureNotes/MER212L12.pdfMER212: Chapter 17 Planar Kinetic Equations of Motion Kinetics of Rigid Bodies

MER212: Chapter 17

Planar Kinetic Equations of Motion

Kinetics of Rigid Bodies Planar Kinetic Equations of Motion

(17.2) E l ’ E ti f M ti Euler’s Equations of Motion

Union CollegeMechanical Engineering

ESC020: Rigid Body Mechanics 1

Euler’s Equations



Newton’s and Euler’s Equations

Newton’s Laws Newton’s Laws

amF

Euler’s Equations

dmdmrMmm

dmm



m

Newton’s and Euler’s Equationsin Cartesian Form

Newton’s Laws Newton’s Laws

yy

xx

amF

amF

Euler’s Lawszz

yy

amF

dmzxdmrIIIIM

dmzydmrIIIIMm m

xxxzyzyxxox

222

222

;

;

dmxydmrIIIIM

dmzxdmrIIIIM

zzzyxyxzzoz

m myyyxzxzyyoy

222;

;



m m

Example 1 A 16x20ft hanger door, A 16x20ft hanger door,

which weights 800 lbs, is supported by two rollers as shown. A force F of 300 lbs is applied to open 300 lbs is applied to open the door. Determine the acceleration of the door and the support forces ppexerted on the door by the two rollers. Neglect frictional forces and the mass of the rollersmass of the rollers



Example 1: Free Body/Mass Acceleration Diagrams



Example 2The rod AB shown has a The rod AB shown has a constant cross section and a mass of 10kg. As a result of the rotation of crank C, rod AB oscillates in a vertical AB oscillates in a vertical plane. In the position shown, its angular velocity ω is 10 rad/s clockwise and its angular acceleration α is 40 angular acceleration α is 40 rad/s2 counterclockwise. Determine the force exerted by the link between the rod and the crank and the force and the crank and the force exerted on rod AB by the pin at support A.



Example 3 A light 100ft cord is wrapped A light 100ft cord is wrapped

around the 32.2 lb spool, which is pinned at C to the cart. The radius of gyration of the cart with respect to the axis normal to the respect to the axis normal to the figure at C is 1.3 ft. The cart without the spool weights 64lbs. The wheels of the cart are small and light, so that friction beneath and light, so that friction beneath them is negligible. The 2 and 3 lb forces are applied to the system at rest. If upon complete unwrapping the cord is to end up unwrapping the cord is to end up between points P and Q in the lower figure, where should C be origionally parked along PQ



Example 2: Free Body Diagram



Example 2: Free Body Diagrams



Example 4 The 32 2 lb The 32.2 lb

particle P rests on the 128.8 lb

l k h plank as shown. If the cord at B suddenly breaks, y ,find the initial acceleration of the particle, and the particle, and the force exerted on it by the bar.



Example 4: FBD/MAD



Documents

MER212: Chapter 17 Kinetics of Rigid Bodiesminerva.union.edu/bucinelr/mer212/LectureNotes/MER212L12.pdfMER212: Chapter 17 Planar Kinetic Equations of Motion Kinetics of Rigid Bodies