dinamika - 6 kinetika benda tegar - impuls momentum
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Materi kuliah dinamikaTRANSCRIPT
1-12-2014
Jurusan Teknik Mesin dan Industri, Fakultas Teknik, Universitas Gadjah Mada
Dinamika TKM 2302 / 3 SKS
Dr. Indraswari Kusumaningtyas
2 Dinamika – Kinetika Benda Tegar – Impuls & Momentum Jurusan Teknik Mesin dan Industri FT UGM
Kinetika Benda Tegar 6 Impuls dan Momentum
This method is well suited to the solution of problems
involving force, velocity and time, particularly if the applied
forces were expressible as functions of the time.
It is the only practicable method for problems involving
impulsive motion and impact, i.e. when interactions between
rigid bodies occur during short periods of time.
3 Dinamika – Kinetika Benda Tegar – Impuls & Momentum Jurusan Teknik Mesin dan Industri FT UGM
Principle of Impulse & Momentum
Consider a rigid body as made of a large number of particles Pi .
4 Dinamika – Kinetika Benda Tegar – Impuls & Momentum Jurusan Teknik Mesin dan Industri FT UGM
The momenta of the particles of a system can be reduced to a
vector attached to the mass center G, equal to their sum:
and a couple equal to the sum of their moments about G,
Principle of Impulse & Momentum
The system of momenta viΔmi
is equivalent to the linear
momentum vector attached
at G and to the angular
momentum couple .
5 Dinamika – Kinetika Benda Tegar – Impuls & Momentum Jurusan Teknik Mesin dan Industri FT UGM
Principle of Impulse & Momentum
Based on the principle of impulse and momentum for plane motion
of rigid body, we have three diagrams.
6 Dinamika – Kinetika Benda Tegar – Impuls & Momentum Jurusan Teknik Mesin dan Industri FT UGM
Principle of Impulse & Momentum
Three equation of motions obtained by:
Summing and equating the momenta and impulses in the x and y
directions.
Summing and equating the moments of these vectors with respect
to any given point.
Can be computed with respect to any points other than G, but consistent.
7 Dinamika – Kinetika Benda Tegar – Impuls & Momentum Jurusan Teknik Mesin dan Industri FT UGM
Principle of Impulse & Momentum Translation
Rectilinear or Curvilinear,
Angular velocity ω = 0
Mass center velocity vG = v
If angular momentum is computed from
some other point A , the moment of the
linear momentum L must be calculated
about that point, so
8 Dinamika – Kinetika Benda Tegar – Impuls & Momentum Jurusan Teknik Mesin dan Industri FT UGM
Principle of Impulse & Momentum Rotation
Centroidal Rotation
Mass center velocity vG = 0
Angular velocity ω
Non-Centroidal Rotation about O
Mass center velocity vG
Angular velocity ω
Computing about O,
9 Dinamika – Kinetika Benda Tegar – Impuls & Momentum Jurusan Teknik Mesin dan Industri FT UGM
System of Rigid Bodies
The principle of impulse and momentum can be applied to an entire
system of connected bodies rather than to each body separately.
This eliminates the need to include interaction impulses which occur
at the connections, since they are internal to the system.
Note that the system's
angular momentum and
angular impulse must be
computed with respect to
the same reference point O
for all the bodies of the
system.
10 Dinamika – Kinetika Benda Tegar – Impuls & Momentum Jurusan Teknik Mesin dan Industri FT UGM
Conservation of Momentum
When no external force acts on a rigid body or a system of rigid
bodies, the system of the momenta at time t1 is equipollent to
the system of the momenta at time t2.
The total linear momentum of the system is conserved in any
direction and its total angular momentum is conserved about
any point.
Conservation of linear momentum
Conservation of angular momentum
11 Dinamika – Kinetika Benda Tegar – Impuls & Momentum Jurusan Teknik Mesin dan Industri FT UGM
Conservation of Momentum
There are cases in which
the linear momentum is
not conserved yet the
angular momentum of
the system is conserved.
This occurs when the
external forces creating
the linear impulse pass
through either the
center of mass of the
body or a fixed axis of
rotation, so the angular
impulse is zero.
12 Dinamika – Kinetika Benda Tegar – Impuls & Momentum Jurusan Teknik Mesin dan Industri FT UGM
Conservation of Momentum
Another classic example
of conservation of angular
momentum. When the
spinning wheel is moved
so its axis of rotation
becomes vertical, the
frictionless turn-table
spins in a direction
opposite to the wheel
(i.e. conserving angular
momentum about the
vertical axis).
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Contoh 1
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Eccentric Impact
Eccentric impact occurs when the line connecting the mass centers
of the two bodies does not coincide with the line of impact.
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Eccentric Impact
Assuming that the bodies are frictionless, we find that the forces
they exert on each other are directed along the line of impact.
Besides the principle of impulse and momentum, we use the
coefficient of restitution:
Study the text book to understand
the method for deriving the
coefficient of restitution.
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Contoh 2
It is normally assumed that the impact creates forces
which are much larger than the non-impulsive weights of
the bodies.
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