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

Objective To introduce the concept of angular impulse and momentum.

Definition Moment = “عزم” = r x F

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

ANGULAR MOMENTUM Angular momentum about point O is defined as the “ moment ” of the particle ’ s linear momentum about O. Angular momentum (H o ) = ( r x mV) 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

Angular Momentum

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

Angular Impulse and Momentum Principles

Scalar Formulation Conservation of Angular Momentum Angular impulse is zero

Example 15-13

Example 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

Example 15-15

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

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