Ch 4 (Centers of Mass and Gravity) B.Sc Mechanics Notes

Introduction to Mechanics (B.Sc.)

In this chapter, we will study the following topics:

the center of mass of a set of particles
cartesian coordinates of the c.m
centroid
the center of mass of a continuous distribution of matter
center of mass of a thin road
center of mass of lamina
center of mass of a solid
symmetry and center of mass
symmetry with respect to a point
symmetry with respect to a line
symmetry with respect to a plane
if a body possess central symmetry, the center of symmetry is the center of mass
the center of mass of the union of any number of disjoint sets of particles
to find the c.m of the set of particles S, S1 when the centers of mass of S and S1 are known
disjoint proper subsets
a thin uniform rod
a uniform rectangular lamina
a uniform wire bent into the form of an isosceles right-triangle
a uniform lamina whose boundary is a parallelogram
a uniform triangular lamina
three uniform rods forming a triangular frame
a uniform tetrahedronal solid
the height of the solid
a right circular solid cone
the symmetry of c.m
a hollow right circular cone
a uniform solid hemisphere
a uniform circular arc
a uniform sector of a circular lamina
center of mass of an arc
centroid of plane region
mass center of a solid of revolution
the mass center of a surface of revolution
theorems of pappus
center of gravity