The center of mass of an object is the single point where the entire mass of the object is considered to be concentrated and acts as if the whole mass were located; it is defined mathematically as the weighted average of every discrete point making up the object. The document discusses center of mass for different geometric objects like cylinders, spheres, and distributed point masses, and explains that finding the center of mass allows predicting the object's motion as if all its mass were concentrated at that point.
this is about center of mass, center of mass for complicated shapes, center of mass of hemisphere, center of mass of many particles, center of mass of solids, center of mass of uniform cylinder, center of mass of uniform rod
this is about center of mass, center of mass for complicated shapes, center of mass of hemisphere, center of mass of many particles, center of mass of solids, center of mass of uniform cylinder, center of mass of uniform rod
This PPT covers relative motion between particles in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.
Fundamentasl of Physics "CENTER OF MASS AND LINEAR MOMENTUM"Muhammad Faizan Musa
9-1 CENTER OF MASS
fter reading this module, you should be able to . . .
9.01 Given the positions of several particles along an axis or
a plane, determine the location of their center of mass.
9.02 Locate the center of mass of an extended, symmetric
object by using the symmetry.
9.03 For a two-dimensional or three-dimensional extended object with a uniform distribution of mass, determine the center
of mass by (a) mentally dividing the object into simple geometric figures, each of which can be replaced by a particle at its
center and (b) finding the center of mass of those particles.
9-2 NEWTON’S SECOND LAW FOR A SYSTEM OF PARTICLES
After reading this module, you should be able to . . .
9.04 Apply Newton’s second law to a system of particles by relating the net force (of the forces acting on the particles) to
the acceleration of the system’s center of mass.
9.05 Apply the constant-acceleration equations to the motion
of the individual particles in a system and to the motion of
the system’s center of mass.
9.06 Given the mass and velocity of the particles in a system,
calculate the velocity of the system’s center of mass.
9.07 Given the mass and acceleration of the particles in a
system, calculate the acceleration of the system’s center
of mass.
9.08 Given the position of a system’s center of mass as a function of time, determine the velocity of the center of mass.
9.09 Given the velocity of a system’s center of mass as a
function of time, determine the acceleration of the center
of mass.
9.10 Calculate the change in the velocity of a com by integrating the com’s acceleration function with respect to time.
9.11 Calculate a com’s displacement by integrating the
com’s velocity function with respect to time.
9.12 When the particles in a two-particle system move without the system’s commoving, relate the displacements of
the particles and the velocities of the particles,
This PPT covers relative motion between particles in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.
Fundamentasl of Physics "CENTER OF MASS AND LINEAR MOMENTUM"Muhammad Faizan Musa
9-1 CENTER OF MASS
fter reading this module, you should be able to . . .
9.01 Given the positions of several particles along an axis or
a plane, determine the location of their center of mass.
9.02 Locate the center of mass of an extended, symmetric
object by using the symmetry.
9.03 For a two-dimensional or three-dimensional extended object with a uniform distribution of mass, determine the center
of mass by (a) mentally dividing the object into simple geometric figures, each of which can be replaced by a particle at its
center and (b) finding the center of mass of those particles.
9-2 NEWTON’S SECOND LAW FOR A SYSTEM OF PARTICLES
After reading this module, you should be able to . . .
9.04 Apply Newton’s second law to a system of particles by relating the net force (of the forces acting on the particles) to
the acceleration of the system’s center of mass.
9.05 Apply the constant-acceleration equations to the motion
of the individual particles in a system and to the motion of
the system’s center of mass.
9.06 Given the mass and velocity of the particles in a system,
calculate the velocity of the system’s center of mass.
9.07 Given the mass and acceleration of the particles in a
system, calculate the acceleration of the system’s center
of mass.
9.08 Given the position of a system’s center of mass as a function of time, determine the velocity of the center of mass.
9.09 Given the velocity of a system’s center of mass as a
function of time, determine the acceleration of the center
of mass.
9.10 Calculate the change in the velocity of a com by integrating the com’s acceleration function with respect to time.
9.11 Calculate a com’s displacement by integrating the
com’s velocity function with respect to time.
9.12 When the particles in a two-particle system move without the system’s commoving, relate the displacements of
the particles and the velocities of the particles,
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Centre of mass
1. Dr.M. ANNIE FREEDA
P.G Assistant in PHYSICS
S.L.B.G.H.S.S., NAGERCOIL
Kanyakumari District
CENTRE OF MASS
2. CENTRE OF MASS
. We could see a large number of objects around us.
. Objects around us consists of large number of particles.
. When an object moves collection of all particles as a system
moves.
. To understand the concept of centre of mass we must know.
1) What is a rigid body.
2) What is a point mass
3) What path does the particles in a body take, while
the body moves
3. A rigid body is the one which maintain its definite and
fixed shape even when an external force acts on it
A point mass is a hypothetical point particle which has
nonzero mass and no size or shape.
4. Let us consider a solid cylinder hollow
cylinder and a sphere moving
Rolling objectsNew folderVID20180816190739.mp4
Rolling objectsNew folderVID20180816191621.mp4
Rolling objectsNew folderVID20180816192031.mp4
5. When a bulk object (say a bat) is thrown at an
angle in air
Actually, only one point takes the parabolic path and all the other
points take different paths. ----- CENTRE OF MASS
6. The center of mass of a body is defined as a point where the
entire mass of the body appears to be concentrated.
.. . ..
7. Let m1, m2, m3 . . . mn be point masses of n particles.
Let, x1, x2, x3 . . . xn be the position of the respective particles
along X-coordinate.
Centre of mass for distributed point
masses
24. Evaluation
1. Define center of mass.
2. Is centre of mass a point or mass?
3. Find out the center of mass for the given geometrical
structures. a) Equilateral triangle b) Cylinder c) Square
