Impulse-Momentum for Rigid Bodies Lecture 31
ME 231: Dynamics HO IG mvd Question of the Day
A slender bar of mass 0.8 kg and length 0.4 m is falling with a velocity v = 2 m/s and angular velocity = 10 rad/s.
Determine the angular momentum HO of the bar about point O.
ME 231: Dynamics Outline for Today
Question ofof the dayday Linear momentum for rigid bodies Angular momentum for rigid bodies Interconnected rigid bodies Conservation of momentum for rigid bodies Answer your questions!
ME 231: Dynamics Recall: Linear Momentum for Particle Systems
Gi mi vi
G B mi vi G B m v i i m 0 d G B m v B m i dt i i G mv G mv ma B F G
ME 231: Dynamics Linear Momentum for Rigid Bodies
Special case of a general system of particles G mv
t G 2 F dt G B F G 1 O 2 t1
t G 2 F dt G B Fx Gx 1 x O x 2 x t1 t2 B F G G F dt G y y 1 y O y 2 y t1
ME 231: Dynamics Recall: Angular Momentum for Particle Systems About the Mass Center G
H m r G i i i i HG B i miri HG B i mi r i HG B i mir B i mi i 0 H B F G i i HG r B mi i B i mi i B M H G G HG B i mi i ME 231: Dynamics Angular Momentum for Rigid Bodies About the Mass Center G linearlinear angular
G mv HG IG
B F G B MG HG
t t G 2 F dt G H 2 M dt H 1 O 2 G 1 O G G 2 t1 t1
ME 231: Dynamics Alternate Angular Momentum for Rigid Bodies About an Arbitrary Point P About a Fixed Point O
P
H P IG mvd HO IO B M H B M P H P O O
t t H 2 M dt H H 2 M dt H P 1 O P P 2 O 1 O O O 2 t1 t1
ME 231: Dynamics Recall: Systems of Interconnected Bodies
free-body diagram kinetic diagram
B F B ma
B M P B IG B mad
ME 231: Dynamics Interconnected Rigid Bodies
combined free-body and momentum diagrams B F G a Gb "
t 2 F dt G O system t1
B M H H " O O a O b
t 2 M dt H O O O system t1
ME 231: Dynamics Recall: Conservation of Momentum for Systems
H H G G O 1 O 2 1 2 H H G 1 G 2
If the resultant external force F is zero, then linear momentum is conserved If the resultant moment about a fixed point O or mass center G is zero, then angular momentum is conserved
ME 231: Dynamics Conservation of Momentum for Rigid Bodies Exactly the same as for particle systems!
H H G G O 1 O 2 1 2 H H G 1 G 2
If the resultant external force F is zero, then linear momentum is conserved If the resultant moment about a fixed point O or mass center G is zero, then angular momentum is conserved
ME 231: Dynamics Impulse-Momentum for Rigid Bodies: Exercise 1
A constant horizontal force P is applied the light yoke attached to the center O of a uniform circular disk of mass m, which is initially at rest and rolls without slipping.
Determine the velocity v of the center O in terms of t.
ME 231: Dynamics Impulse-Momentum for Rigid Bodies: Exercise 2
A uniform circular disk has a mass of 25 kg and is mounted to a rotating bar in three different ways and O = 4 rad/s
Determine the angular momentum HO of the disk about point O for each case. 8 rad/s ME 231: Dynamics Impulse-Momentum for Rigid Bodies: Exercise 3
Fully extended the diver’s 80-kg body has a angular velocity of 0.3 rev/s.
Determine the angular velocity later when the diver assumes a tuck position.
ME 231: Dynamics Outline for Today
Question ofof the dayday Linear momentum for ririgidgid bodiesbodies AngularAngular momentum for ririgidgid bodiesbodies InterconnectedInterconnected ririgidgid bbodiesodies Conservation ofof momentum fforor ririgidgid bodiesbodies Answer your questions!
ME 231: Dynamics For Next Time…
Exam 2.a on Friday (11/9) Homework #10 due on Monday (11/12) Homework #11 due on Wednesday(11/14) Read Chapter 8, Sections 8.2 & 8.3
ME 231: Dynamics