Jumat, 13 Januari 2012

Modul Experiment : Determine Angular Momentum

DWI WIJI UTOMO (083184003) AND MUHAMMAD HABIB (083184005)
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

1.       How can we show the angular momentum?
2.       How can we calculate the amount of angular momentum?

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 = 2πf

L = angular momentum
I = moment of Inertia
m = mass of object
l = length of object

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.

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
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.

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

a.       Data manipulation voltage of power supply
Voltage  (V)
Time (s)
Length of rigid bar (cm)

b.       Data manipulation length of rigid bar

Voltage  (V)
Time (s)
Length of rigid bar (cm)

Halliday, Resnick. 1988. Fisika Jilid 1. Jakarta Erlangga