6.1.1 The Center of Mass of a System of Particles Flashcards
The Center of Mass of a System of Particles
- The center of mass of any object is a position vector, , that represents the location where you can assume all the object’s mass is concentrated.
- The mathematical definition of the center of mass:
- The physical location of the center of mass is independent of the coordinate system you choose.
- Every object acts as if its mass were concentrated at its center of mass.
Given a system of particles, which of the following must we do to find the center of mass of the system?
Set up coordinates for the particles.
Locate the center of mass of the following system:
The coordinates are as follows:
(L/8, L/4)
Locate the center of mass of the following system:
The coordinates are as follows:
(L/4, 0)
Which of the following statements about the center of mass of a system of particles is untrue?
The center of mass is the geometrical center of the system.
Locate the center of mass of the following system:
The coordinates are as follows:
(L/6, 0)
Which of the following is the formula for the center of mass of a system of particles (mi, ri), where mi and ri stand for the mass and position of particle i respectively?
rcm = m1r1 + m2r2 + … mnrn / m1 + m2 + … + mn
Locate the center of the mass of the following system:
The coordinates are as follows:
(3L/4, 0)
Which of the following is true for the following system of particles?
Assume each particle has the same mass and the four lines are the same length (i.e., the particles are equidistant from the center).
The center of mass of this system is on the central particle.
A system is composed of two particles. One particle is located at (1, 1) and has a mass of 3.4 kg; the second particle is located at (−6.4, 5.8) and has a mass of 5.0 kg. Where is the x-component of the center of mass of the system located?
-3.4
