1. King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 21

2. Objective To introduce the concept of angular impulse and momentum.

3. Definition Moment = “عزم” = r x F Angular momentum about point O is defined as the “ moment ” of the particle ’ s linear momentum about O. Angular momentum (H o ) = moment of linear momentum ( r x mV)

4. Line of action of the force F Torque = Fl l Torque” Moment” = F l Torque = F l F l l Cheater Pipe F

5. ANGULAR MOMENTUM For a point object the angular momentum is r m v Units - kg. m 2 /s or sl. ft 2 /s It is a vector. Here the vector is pointing toward you. Using right-hand rule

6. Angular Momentum

7. Relation Between Moment of a Force and Angular Momentum Resultant moment = Rate of change of angular momentum Resultant force = Rate of change of linear momentum

8. System of Particles Internal force cancel each other Sum of the moments about O of all the external forces acting On a system of particle = rate of change of the total angular Momentum of the system of particles about point O

9. Example 15-12

10. Angular Impulse and Momentum Principles

11. Scalar Formulation Conservation of Angular Momentum Angular impulse is zero

12. Example 15-13

13. Example 15-14 W = 0.8 Ib Smooth table r 1 =1.7 ft v 1 = 4 ft/s v c =6ft/s v 2 = ? at (r 2 )= 0.6ft Work done = ? Work Done

14. Example 15-15

15. Problem 15-101 m = 400 g v 1 = 2 m/s M = 0.6 N.m v 2 =? t = 3 s

16. Problem 102 m = 5-Ib v 1 = 0 ft/s M = ( 0.5 t + 0.8 ) Ib.ft v 2 = ? t = 4 s