Transcript Momentum Notes

Momentum/Collisions
Momentum
"An object in motion tends to
continue in constant motion unless
acted upon by an outside force."
 This tendency, outlined in Newton's
first law, is known as momentum.
How strong this tendency is depends
upon the amount of inertia the object
has and its velocity.

Momentum
The more inertia (mass) an object
has, or the greater its velocity, the
stronger its tendency to continue
moving in constant motion, and so
the greater its momentum.
 momentum=mass x velocity
 p=mv
 The units on this would be kgm/s or
a Ns.—see p. 245

Conservation of Momentum

Conservation of momentum: Within
a system the total amount of
momentum remains constant.


pi = p f
mivi = mfvf
Conservation of Momentum


In a collision between objects the
total sum of momentum of all objects
before the collision is equal to the
total sum of momentum of all objects
after the collision.
pai + pbi = paf + pbf
Collisions
During a collision, momentum is
transferred from one object to
another. There are two main
categories of collisions:
 Elastic


Inelastic
Elastic Collisions


Elastic: in which the
shape of the objects is
maintained. In an
elastic collision the
objects remain
separated after the
collision.
Kinetic energy is
conserved in an elastic
collision, but not in an
inelastic collision.
Inelastic Collisions


Inelastic: in which the
shape of the objects is
changed or deformed (Car
crash, two balls of clay
hitting one another) or in
which they stick together
(two train cars coupling,
bug hitting a windshield.)
In a perfectly inelastic
collision The objects only
have one final mass and
one final velocity because
they are now connected.
Impulse
In order to change an object's
momentum an outside force must
act on it for a certain amount of
time. This change in momentum is
known as an impulse.
 The units on this would be Ns.

FΔt= Δ p=mvf-mvi

(known as Impulse-Momentum
Theorum)
Impulse


A specific change
in momentum may
take place over a
long period of time
thereby creating a
small force, or can
take place in a
short period of
time creating a
large force.
—see p. 251, 252
Angular Momentum
The rotational version of linear
momentum is called angular
momentum, and is determined by
the mass, shape, and angular
velocity of the object.
 It is a separate quantity than linear
momentum

Angular Momentum

Angular momentum is represented
by “L”, and can be calcuated by:

L=Iω
Remember, I represents Moment of
Inertia, and ω represents angular
velocity
Angular Momentum

Angular momentum is conserved for
any closed system, which means that
if the moment of inertia is increased,
the angular velocity will decrease,
and vice versa (see p. 254)
Angular Momentum


Another implication
regards the
direction of angular
momentum of a
spinning object.
The actual
direction is not in
the same direction
as the linear
motion, but along
the axis of
rotation.
Angular Momentum


According to L =
Iω, if the angular
velocity or the
moment of inertia
is high, than the
angular
momentum is high
Object will
therefore resist
any change in
direction (see p.
256)