DETERMINE THE ANGULAR MOMENTUM
DWI
WIJI UTOMO (083184003) AND MUHAMMAD HABIB (083184005)
PHYSICS
DEPARTMENT, MATHEMATIC AND SCIENCE FACULITY
STATE UNIVERSITY OF SURABAYA
A. OBJECTIVE
1. Determine
the amount of angular momentum of object
2. Determine
the relation between voltage of source with its amount angular momentum
3. Determine
the relation between the length of object with its own angular momentum
B. PROBLEM
1. How
can we show the angular momentum?
2. How
can we calculate the amount of angular momentum?
C. THEORY
The angular momentum of a system
of particles (e.g. a rigid body) is the sum of angular moment of the individual
particles. For a rigid body rotating around an axis of symmetry (e.g. the fins
of a ceiling fan), the angular momentum can be expressed as the product of the
body's moment of inertia I (a measure of an object's resistance to changes in
its rotation rate) and its angular velocity ω:
|
L
= I ω
I
= 1/12 ml2
ω
= 2Ï€f
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L
= angular momentum
I
= moment of Inertia
m
= mass of object
l =
length of object
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In this way, angular momentum is
sometimes described as the rotational analog of linear momentum.Angular momentum
is conserved in a system where there is no net external torque, and its
conservation helps explain many diverse phenomena. For example, the increase in
rotational speed of a spinning figure skater as the skater's arms are
contracted is a consequence of conservation of angular momentum. The very high
rotational rates of neutron stars can also be explained in
terms of angular momentum conservation. Moreover, angular momentum conservation
has numerous applications in physics and engineering (e.g. the gyrocompass).
As seen from the definition, the
derived SI units of angular momentum are newton metre seconds (N·m·s or kg·m2s−1)
or joule seconds. Because of the cross product, L is a pseudovector
perpendicular to both the radial vector r and the momentum vector p and it is
assigned a sign by the right-hand rule.
For an object with a fixed mass
that is rotating about a fixed symmetry axis, the angular momentum is expressed
as the product of the moment of inertia of the object and its angular velocity
vector:
where
I is the moment of inertia of the object (in general, a tensor quantity), and ω
is the angular velocity.
Angular momentum is also known as
moment of momentum.It is misconception that angular momentum is zero for
particle in rectilinear motion or for body in pure translationAngular momentum
of a collection of particlesIf a system consists of several particles, the
total angular momentum about a point can be obtained by adding (or integrating)
all the angular momenta of the constituent particles.Angular momentum
simplified using the center of mass
It
is very often convenient to consider the angular momentum of a collection of
particles about their center of mass, since this simplifies the mathematics
considerably. The angular momentum of a collection of
particles is the sum of the angular momentum of each particle:
where
Ri is the position vector of particle i from the reference point, mi is its
mass, and Vi is its velocity.
So that the total angular
momentum with respect to the center isThe first term is just the angular
momentum of the center of mass. It is the same angular momentum one would
obtain if there were just one particle of mass M moving at velocity V located
at the center of mass. The second term is the angular momentum that is the result
of the particles moving relative to their center of mass. This second term can
be even further simplified if the particles form a rigid body, in which case it
is the product of moment of inertia and angular velocity of the spinning motion
(as above). The same result is true if the discrete point masses discussed
above are replaced by a continuous distribution of matter.
D.
VARIABLES
Experiment 1:
Variable of manipulation :
voltage
Variable of response : time
Variable
of controls : length of rigid bar, rotation, mass of rigid bar
Experiment
2:
Variable
of manipulation : length of rigid bar
Variable
of response : time
Variable
of controls : voltage, rotation, mass of rigid bar
E.
PROCEDURE OF EXPERIMENT
a. Stringing
up tool as on figure 2.
b.
Put together object on motor and object with
constant mass.
c.
Turning around
dynamo and accounting total object lap as much that 20 laps (lap includes in
variable control)
d.
Noting time
required just for does 20 laps.
e.
Go over for
object length that variably but its mass with.
F. TOOLS
AND MATERIALS
a. Power
supply
b. Motor
DC 12volt
c.
Stick that
fixed its mass and can be change its length (m= 143.99 gram).
d. Stopwatch
figure
2: design of instrument
G.
DATA AND ANALYSE
a.
Data
manipulation voltage of power
supply
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NO
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Voltage (V)
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Time
(s)
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Rotary
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Length
of rigid bar (cm)
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b.
Data
manipulation length
of rigid bar
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NO
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Voltage (V)
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Time
(s)
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Rotary
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Length
of rigid bar (cm)
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LITERATURE
Halliday, Resnick. 1988. Fisika Jilid 1. Jakarta Erlangga
habib-fisika.blogspot.com
kambing-fisika.blogspot.com
