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King Fahd University of Petroleum & Minerals

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King Fahd University of Petroleum & Minerals

Mechanical Engineering

Dynamics ME 201

BY

Dr. Meyassar N. Al-Haddad

Lecture # 21

- To introduce the concept of angular impulse and momentum.

- 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