Ch 8: Systems of Particles and Conservation of Linear Momentum
Q: In terms of physics, what does work mean? What does work cause?
Q: In terms of physics, what does momentum mean? What does momentum
cause?
Q: What does the work-energy theorem say?
Q: What does the impulse-momentum theorem say?
DEF: Momentum = linear momentum = mass x linear velocity = m  v
DEF: Momentum of a system of particles = the vector sum of all of the
momenta of the individual particles in the system = ∑ m  v
Q: Why would the vector sum be relevant for the momentum of a system of
particles?
A: Because velocity is a vector
Q: What can you say about a system’s momentum if the net force acting on
the system is zero? Why?
A: It has to be constant because if Fnet is zero, there is no acceleration, thus,
the velocity stays constant, as well.
Q: What does it mean to say the energy of an isolated system is conserved?
Q: What does it mean to say the momentum of an isolated system is
conserved?
Q: How does this translate from Ch 6-7, and from M-S-T Physics?
A: Ein = Eout
m
v m
=
v
Here’s some amazing stuff that NASA did in 2015 re:
conservation of momentum!! http://www.nasaspaceflight.com/2015/04/evaluatingnasas-futuristic-em-drive/
8.1 Center of Mass
Q: What is torque?
A: A rotating force = a force of rotation applied over a distance
Q: Does torque do work?
A: Yep, it’s Force • distance. The force just happens to cause the object /
system to rotate
Q: What is the center of mass?
DEF: Center of mass of a system = c.o.m. = com = cm = c.o.g = cog = cg = M =
the bulk motion of the system = the torque balance point of the system.
Q: Does the com (M) for an object have to be located on the object?
Q: If you cut a broom in half, which half weighs morr – the “broom” part or
the handle part?
Q: How do you find the com (M) for a broom?
Q: If you cut a broom at the balance point, which part weighs morr – the
“broom” part or the handle part?
Figure 8-1
Figure 8-2
Figure 8-3
In Fig 8-1 above, if m1 = m2, then the com (M) is in the middle. In Fig 8-2, the
com is toward m1. What if you can’t tell by looking?
To sum it up (), if you find the M for all of the x’s, as well as the y’s and z’s,
you end up with the overall M for the entire system. Morrover, you can rewrite
that in terms of the position and unit vectors. (Your favorite, I know! )
If you’re trying to determine the M for a continuous object, you can use
where dm is an element of mass located at position r, as shown in Fig 8-4 below
See Ex 8-1, p 219-220
Figure 8-3
In a water molecule with a mass of 18 u (16 u from O and 1 u from each H),
the H’s are 96 pm apart (96 x 10-12 m) from the O, and separated from the O
by an angle of 104.50. Find the com of the molecule. (See Ex 1 and Fig 8-3
above.)
You Try Ex 8-2, p 220-221
Gravitational PE of a System
The gravitational PE of a system in a uniform gravitational field is the same as
if all of the mass were concentrated at the center of mass
8.2 C.O.M. By Integration
This section is optional. However, if you’d like to read it, it’s quite short, and
being that you all know calc well, you may choose to do your problems this
way, when applicable. 
8.3 Motion of the C.O.M.
For any object set in rotational motion, the path of the com is always parabolic.
Cool, huh!?
Take 2 minutes, and read p 223-224. (Eq 8-5 is on p 218.)
Q: Can you explain the calculus behind these three equations that relate the
com to velocity, acceleration, and N2?
A: They are simply the 1st and 2nd derivatives wrt position / time / (mass). 
See ex’s 8-3 – 8-5. Try ‘em now! 