Patel, Kinal – Homework 17 – Due: Nov 6 2007, 7:00 pm – Inst: D Weathers
1
This
printout
should
have
9
questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
The due time is Central
time.
001
(part 1 oF 1) 10 points
A solid cylinder oF mass
M
= 23 kg, radius
R
= 0
.
34 m and uniForm density is pivoted on
a Frictionless axle coaxial with its symmetry
axis.
A particle oF mass
m
= 3
.
1 kg and
initial velocity
v
0
= 18 m
/
s (perpendicular
to the cylinder’s axis) ±ies too close to the
cylinder’s edge, collides with the cylinder and
sticks to it.
BeFore the collision, the cylinder was not ro
tating. What is its angular velocity aFter the
collision?
Correct answer: 11
.
2409 rad
/
s.
Explanation:
Basic Concept:
Conservation oF Angu
lar Momentum,
L
particle
z
+
L
cylinder
z
= const
.
The axle allows the cylinder to rotate without
Friction around a fxed axis but it keeps this
axis fxed. Let the
z
coordinate axis run along
this axis oF rotation; then the axle may exert
arbitrary torques in
x
and
y
directions but
τ
z
≡
0. Consequently, the
z
componenent oF
the angular momentum must be conserved,
L
z
= const, hence when the particle collides
with the cylinder
L
before
z,
part
+
L
before
z,
cyl
=
L
z,
net
=
L
after
z,
part
+
L
after
z,
cyl
.
BeFore the collision, the cylinder did not
rotate hence
L
before
z,
cyl
= 0
while the particle had angular momentum
~
L
before
part
=
~r
×
~
P
0
=
×
m~v
0
.
Both the radiusvector
and the velocity
~v
0
oF the particle lie in the
xy
plane (
⊥
to the
z
axis), and according to the picture, at the
moment oF collision the radius vector has mag
nitude


=
R
equal to the cylinder’s radius
and direction perpendicular to the particle’s
velocity.
Hence, its angular momentum is
parallel to the
z
axis and has magnitude

~
L
before
part

=
L
before
z,
part
=
Rmv
0
.
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 Spring '07
 Weathers
 Angular Momentum, Work, Moment Of Inertia, Correct Answer, kg, patel

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