AP Physics Chapter 9-10 Key Equations and Ideas
Momentum and Collisions
Center of mass:
1
xcom 
M
xcom 


p  mv

 dp
F 
dt
dp
When Fnet = 0,
 0
dt
v1f 
m1  m2
m1  m2
v1i 
1
M
n
m x
(discrete particles)
 x dm
(distributed mass)
i i
i 1
 F(t) dt
p  p
F t = p = J (impulse)
J
n
n
 pf = pi (always) 
2m2
m1  m2
v2i
v2f 
ii
fi
i 1
2m1
m1  m2
i 1
v1i 
m2  m1
m1  m2
v2i
Kf = Ki (elastic collisions only)
Key Ideas:

The center of mass of a body or a system of bodies is the point that moves as though all
the mass were concentrated there and all external forces were applied there.

In center of mass problems, make full use of the symmetry of the object (i.e. about a
point, a line or a plane). If the object can be divided into several parts, treat each of
these parts as a particle, located at its own center of mass. Choose your axes wisely.

The time rate of change of the momentum of a particle is equal to the net force acting on
the particle and is in the direction of that force.

The linear momentum of a system of particles is equal to the product of the total mass of
the system and the velocity of the center of mass.

If no net external force acts on a system of particles, the total linear momentum of the
system cannot change.

If the component of the net external force on a closed system is zero along an axis, then
the component of the linear momentum of the system along that axis cannot change.

Conservation of momentum always holds in a closed (i.e. no matter passes in or out) and
isolated (i.e. no external forces) system. Momentum is conserved in each dimension!!

A collision is an isolated event in which two or more bodies exert a relatively strong force
on each other for a relatively short time. Momentum is always conserved. Kinetic energy
is only conserved in a perfectly elastic collision.