1. CH 8: Systems of Particles and Extended objects

2. Center of Mass (Center of Gravity)
Center of mass – Average location of the mass of an object if all the mass is concentrated at a single point. The center of mass does not have to be inside the object!
Center of gravity – Average location of the weight of an object if all the weight is concentrated at a single point. ri
rcm
ri – Position of small part of the total mass.
rcm – Position of the center of mass.
Dmi or dmi – Small part of total mass.
M – Total mass.
DWi or dWi – Small part of the total weight.
W – Total weight.
Talk about importance of center of mass in balance. Example: Person bends over and sticks their butt out. Why?
Discrete particles
The derivation of these equations involves Torque, which we will learn about in the next chapter.
Continuous object

3. The position of the center of mass rcm can be separated into x, y and z components.
If the position changes in time, we can look at the velocity of the center of mass. or
The momentum of the center of mass is equal to the sum of the momentums of each part of the mass.
Notice that:
This is not conservation of momentum!!

4. Example: What is the velocity of the center of mass of a system of 3 particles where:

5. Example: Determine the x-component of the center of mass of a thin triangular object. The object has a thickness t and the mass is uniformly distributed throughout the object. y x
Total mass of the object
Small part of the mass of the object b y dx
Relationship between x and y a
A similar analysis would be done to determine the y-component of the center of mass.