dm M (mass of the body)
1
rCM rdm.
M
1 1 2 2 3 3.......... n n
CM
m v m v m v m v
v
M
1 1 2 2 3 3.......... n n
CM
m a m a m a m a
a
M
(I) Addition of mass
Due to addition of mass, the C.M of a system
generally shifts towards or into the region
where mass is added. If C 1 is C.M before
addition and C 2 is the C.M of added mass
and C C d1 2 ,then
int
shift added ,
ial added
m d
X
M m
C.M shifts
towards the side of added mass.
(II) Removal of mass
Due to removal of mass the C.M of a system
shifts away from the region where mass is
removed. If C 1 is C.M of the body before
removal and C 2 is the C.M of the removed part
and C C d1 2 then
removed
shift
initial removed
m d
X
M m
‘’ indicates CM shifts opposite to the side of
removed mass
ext
dP
F
dt
If ext^0 ; constant
dP
F P
dt
P P P 1 2 ......... Pn constant.
Impulse of a force F acting on a body is defined
as:-
J
= Fdt
=
dv
m
dt
dt =m dv
J m v v ( 2 1 )
It is also defined as change in momentum
J P
J F dt P P P f i
Impulse on a body for a time interval is equal to
the area under force time (F-t) graph in the same
time interval.
It is a vector quantity.
Magnitude is equal to area under the F-t. graph.
J = Fdt = Fav (^) dt = F tav
Collision is an event in which a strong force acts
between two or more bodies for a short time, which
results in change of their velocities.
The line passing through the common normal
to the surfaces in contact during impact is called
line of impact. The force during collision acts
along this line on both the bodies.
Line of impact in different collisions
(i) Two balls A and B are approaching each other
such that their centres are moving along line
CD.
4. Velocity of centre of mass of a system
5. Acceleration of centre of mass of system
6. Shift in the position of centre of mass
7. Conservation of momentum
8. Impulse
Instantaneous Impulse :
9. Collision
10. Line of Impact
11. Elastic collision
Head on Collision
In an elastic collision, the particle regain their
shape and size completely after collision, i.e., no