ATHS
Ch.9 ( Momentum and its Conservation )
G11-CC
Momentum (p)
1- All moving objects can be described by a quantity of motion called
linear momentum.
2- Momentum (p) for objects with mass is a vector quantity in the
direction in which the object is moving.
3- Momentum depends on the mass of the object (increases with
increasing mass) and on the velocity of the object (increases with
increasing velocity),
p  mv
Linear momentum
( Kg.m/s )
mass
( Kg )
velocity
( m/s )
4- There is no standard unit of momentum;
the units are those of the product of mass and velocity, kg.m/s
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Conservation of linear momentum theory
The conservation of linear momentum principle states that :
The total (net) momentum change within a system is equal to the total
momentum transfer into or out of the system.
This can be mathematically represented by:
p  pin  pout
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Change in Momentum and Impulse
12-
Linear momentum is always conserved for all types of interactions
and for both open and closed systems.
Change in momentum ∆p = pf – pi = mvf – mvi = m (vf – vi )= m∆v
3- Impulse ( the total momentum transfer into or out of the system ) is
equal to the change in momentum for the system.
Impulse = Fave ∆t
the vector sum of the external forces (net force)
Impulse = Fave ∆t = ∆p = pf – pi = mvf – mvi = m (vf – vi ) = m∆v
* Impulse-momentum theorem states that :
The impulse of an object is equal to the object’s final momentum
minus the object’s initial momentum.
F
I = pf – pi
4-
I = ∆p = area under ( F – t ) graph.
t
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9.2 Conservation of momentum
*Law of conservation of linear momentum : states that :
For any closed isolated system, momentum is conserved ( doesn’t
change )
Isolated system : the system on which the net force is zero.
Where momentum is conserved.
Before collision
pi
=
after collision
pf
( m1v1 + m2v2 )i = ( m1v1 + m2v2 )f
Types of collisions
Type of Collision
Elastic Collision
Inelastic Collision
Perfect Inelastic
Collision
Momentum
Conserved
pi = pf
Conserved
KEi = KEf
Conserved
pi = pf
Not conserved
KEi ≠ KEf
Not conserved
pi ≠ pf
Not conserved
KEi ≠ KEf
Kinetic Energy
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Momentum and Newton’s Laws
Impulse = Fave ∆t = ∆p
1. The vector sum of the external forces (net force) acting on an object causes the
object’s momentum to change. The average force multiplied by the time interval
is equal to the momentum
v
( Newton’s second law of motion )
Fnet  Fave  m
 ma
t
2. If there are no external forces acting on an object, the object’s momentum (and
therefore its motion) cannot change.
Then the object will be at rest or moving with a constant speed for ever without
change ( Newton’s first law of motion )
3. Interaction forces between two objects cannot change the total momentum of the
objects, since these forces would exist even if the system were isolated ( net
forces = 0 ). Consequently, when two objects interact, the force on one object is
equal in magnitude but opposite in direction to the force on the other object. This
is the origin of Newton’s third law.