King Fahd University of Petroleum & Minerals

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

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

ANGULAR MOMENTUM • Angular momentum about point O is defined as the “moment” of the particle’s linear momentum about O. • Angular momentum (Ho) = ( r x mV) v m Units - kg.m2/s or sl.ft2/s It is a vector. Here the vector is pointing toward you. Using right-hand rule r

Angular Momentum

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

Angular Impulse and Momentum Principles

Scalar Formulation • Conservation of Angular Momentum • Angular impulse is zero

Example 15-13

Example 15-14 W = 0.8 Ib Smooth table r1=1.7 ft v1= 4 ft/s vc=6ft/s v2= ? at (r2)= 0.6ft Work done = ? Work Done

Problem 15-101 m = 400 g v1= 2 m/s M = 0.6 N.m v2=? t = 3 s

Problem 102 W = 5-Ib v1 = 0 ft/s M = ( 0.5 t + 0.8 ) Ib.ft v2= ? t = 4 s

Thank You

King Fahd University of Petroleum & Minerals