Download Statics 210 Chapters 2.1 – 2.3

ENGR 215 ~ Dynamics
Sections 15.5 – 15.7
Angular Momentum
• “Moment” of the
particle’s linear
momentum about
Point O.
• Scalar Formulation
– If the particle is
moving along a curve
lying in the x-y plane.
H O z  (d )(mv)
Angular Momentum
• Vector Formulation
– If the particle is
moving along a space
curve.
H O  r  mv
Lecture Example 1: Determine the angular
momentum HO of the particle about Point O.
Relation between Moment of a Force
and Angular Momentum
Relation between Moment of a Force
and Angular Momentum
• The time rate of
change of a particle’s
angular momentum is
equal to the torque
acting on it.

M

H
 O O
• The time rate of
change of a particle’s
linear momentum is
equal to the force
acting on it.

F

L

Angular Impulse & Momentum Principles
dH O

 M O  H O  dt
 M O dt  dH O
t2
M
O
dt  (H O ) 2 (H O )1
t1
t2
(H O )1    M O dt  (H O ) 2
t1
t2
Angular Impulse    M O dt
t1
t2
   (r  F ) dt
t1
Linear and Angular Impulse
t2
mv1    Fdt  mv 2
t1
t2
(H O )1    M O dt  (H O ) 2
t1
Conservation of Angular Momentum
• When the angular impulses acting on a particle
are all zero during a time from t1 to t2, angular
momentum is conserved.
(H O )1  (H O ) 2
Lecture Example 2: A 4-lb ball is traveling around a circle
of radius r = 3 ft with a speed (vb)1 = 6 ft/s. If the cord is
pulled through the hole with a constant speed, determine
the speed of the ball when r = 2 ft.
Also, how much work had to be done to pull down the
cord?
Lecture Example 3: The 800-lb roller-coaster starts from
rest on the track having the shape of a cylindrical helix. It
the helix descends 8 ft for every revolution, determine the
time required for the car to attain a speed of 60 ft/s.
Neglect friction and the size of the car,