Download Center of Mass Notes

Center of Mass Notes
The center of mass of a system of particles is a specific point at which, for many purposes, the
system's mass behaves as if it were concentrated.
The center of mass is a function only of the positions and masses of the particles that comprise
the system. In the case of a rigid body, the position of its center of mass is fixed in relation to the
object (but not necessarily in contact with it).
In the case of a loose distribution of masses in free space, such as, say, shot from a shotgun,
the position of the center of mass is a point in space among them that may not correspond to
the position of any individual mass.
In the context of an entirely uniform gravitational field, the center of mass is often called the
center of gravity — the point where gravity can be said to act.
What is the center of mass of the system below above?
xcm
origin
m1
m2
x1
m1=5.0 kg
x1=12.0 m
Equation:
m2=2.0 kg
x2=6.0 m
xcm = (m1x1 + m2x2)
(m1 + m2)
x2
xcm = 4.8m
What if the objects are located on two axis?
Same equation as above, but for y (instead of x)
What would happen if the center of mass was moving?
Equation:
xcm = (m1Δ x1 + m2Δx2)
(m1 + m2)
The motion obviously occurs over time. To show the velocity of the center of
mass, divide the displacement by the time to get
vcm = (m1v1 + m2v2) Look at figure 7.18 on page 213
(m1 + m2)
Homework: 41-44 on page 220 and chess board problem from last week’s
Equation:
worksheet AND read chapter 5; sections 5.1-5.3, 5.5-5.6