Outline Of The Presentation
• Centre Of Mass Frame
• Conservation Of Momentum
• Types Of Collision
Centre Of Mass Frame
A reference frame with its origin at the centre of
mass of the system is called centre of mass
reference frame or C frame of reference.
Why Reference Frame?
• It helps us to describe the kinematics of an object
• Geometric description of a motion
Law of Conservation of Momentum:
• In a closed and isolated system, the total momentum of the objects
before a collision is equal to the total momentum of the objects after
the collision.
=>Pi = Pf
What is Closed and Isolated system?
• Matter and energy do not enter or leave the system
• No net outside forces act on the system
=> Fext = 0 , dp/dt=0
p -> constant
Centre Of Mass Frame
y
Properties
1. Origin -> Centre of mass
2. RCM = 0
3. VCM = 0
4. PCM = 0
5. Also called Zero
Momentum reference
S
frame
S’
m1
r1’
CM
r2’
r1
m2
R
r2
x
Let’s Recall
Elastic Collision
Momentum -> Conserved
Kinetic Energy -> Conserved
Inelastic Collision
Momentum -> Conserved
Kinetic Energy -> Not Conserved
Example
• Velocity of m1 is 10 m/s and m2 is at rest in
with respect to origin.
• Find :
The total momentum with respect to C Frame
Analyse the collision (C frame)
Before
After Collision
Collision
Example: Inelastic collision in C frame
V1cm = V1 - Vcm
V2cm = V2 - Vcm
V1cm = (10 – 2.86) = 7.14 m/s
V2cm = -2.86m/s
CM
m1
m2
5 kg
2 kg
Vcm = m1v1 + m2v2/m1+m2=20/7
VCM = 2.86 m/s
Vf = 0 m/s
Total momentum = {2 x 7.14} + {5 x (-2.86)} => PCM= 0
 called Zero Momentum reference frame
Take Away
• In C frame:
1. Origin in centre of mass
2. Frame may move with Centre Of Mass
• In all frames:
1. Momentum is conserved only for closed
and isolated system
Any Questions?
Thank You