- CENTER OF MASS
- CENTER OF MASS OF A SYSTEM OF 'N' DISCRETE PARTICLES
- POSITION OF COM OF TWO PARTICLES
- CENTER OF MASS OF A CONTINUOUS MASS DISTRIBUTION
- CENTER OF MASS OF A UNIFORM ROD
- CENTER OF MASS OF A SEMICIRCULAR RING
- CENTER OF MASS OF SEMICIRCULAR DISC
- CENTER OF MASS OF A SOLID HEMISPHERE
- CENTER OF MASS OF A HOLLOW HEMISPHERE
- CENTER OF MASS OF A SOLID CONE
- CENTER OF MASS OF SOME COMMON SYSTEMS
- MOTION OF CENTER OF MASS AND CONSERVATION OF MOMENTUM
- Accelerat ion of center of mass of system
- Motion of COM in a moving system of particles
- COM moving with acceleration
- Momentum Conservation
- IMPULSE
- Impulsive force
- Impulsive Tensions
- COLLISION OR IMPACT
- Classification of collisions
- On the basis of energy
- Examples of line of impact and collisions based on line of impact
- COEFFICIENT OF RESTITUTION
- Important Point
- Collision in two dimension
- VARIABLE MASS SYSTEM
- Rocket propulsion
- LINEAR MOMENTUM CONSERVATION IN PRESENCE OF EXTERNAL FORCE
- ARCHIMEDES PRINCIPLE

Every physical system has associated with it a certain point whose motion characterises the motion of

the whole system. When the system moves under some external forces, then this point moves as if the

entire mass of the system is concentrated at this point and also the external force is applied at this

point for translational motion. This point is called the center of mass of the system

Read moreCENTER OF MASS OF A SYSTEM OF 'N' DISCRETE PARTICLES

Read moreCenter of mass of two particles of masses m1 and m2 separated by a distance r lies in between the

two particles. The distance of center of mass from any of the particle (r) is inversely proportional

to the mass of the particle

Read moreCENTER OF MASS OF A CONTINUOUS MASS DISTRIBUTION

Read moreSuppose a rod of mass M and length L is lying along the x-axis with its one end at x = 0 and the

Read moreFigure shows the object (semi circular ring). By observation we can say that the x-coordinate of

the center of mass of the ring is zero as the half ring is symmetrical about y-axis on both sides of

the origin. Only we are required to find the y-coordinate of the center of mass.

Read moreFigure shows the half disc of mass M and radius R. Here, we are only required to find the ycoordinate

of the center of mass of this disc as center of mass will be located on its half vertical

diameter. Here to find ycm, we consider a small elemental ring of mass dm of radius x on the disc

(disc can be considered to be made up such thin rings of increasing radii) which will be integrated

from 0 to R. Here dm is given as

Read moreThe hemisphere is of mass M and radius R. To find its center of mass (only y-coordinate), we

consider an element disc of width dy, mass dm at a distance y from the center of the hemisphere.

The radius of this elemental disc will be given as

Read moreA hollow hemisphere of mass M and radius R. Now we consider an elemental circular strip of

angular width d? at an angular distance ? from the base of the hemisphere. This strip will have an

area.

Read moreA solid cone has mass M, height H and base radius R. Obviously the center of mass of this cone

will lie somewhere on its axis, at a height less than H/2. To locate the center of mass we consider

an elemental disc of width dy and radius r, at a distance y from the apex of the cone. Let the mass

of this disc be dm, which can be given as

Read moreThe center of mass lies closer to the heavier mass

Read moreHere numerator of the right hand side term is the total momentum of the system i.e., summation

of momentum of the individual component (particle) of the system

Hence velocity of center of mass of the system is the ratio of momentum of the system to the mass of the

system.

Read moreAccelerat ion of center of mass of system

Read moreMotion of COM in a moving system of particles

Read moreIf an external force is present then COM continues its original

motion as if the external force is acting on it, irrespective of

internal forces.

Example:

Read moreThe total linear momentum of a system of particles is equal to the product of the

Read moreImpulse applied to an object in a given time interval can also be

calculated from the area under force time (F-t) graph in the same

time interval.

Read moreA force, of relatively higher magnitude and acting for relatively shorter time, is called impulsive force.

An impulsive force can change the momentum of a body in a finite magnitude in a very short time

interval. Impulsive force is a relative term. There is no clear boundary between an impulsive and Non-

Impulsive force

Read moreWhen a string jerks, equal and opposite tension act suddenly at each end. Consequently equal

and opposite impulses act on the bodies attached with the string in the direction of the string.

There are two cases to be considered.

Read moreCollision is an event in which an impulsive force acts between two or more bodies for a short time,

which results in change of their velocities.

Read moreClassification of collisions

On the basis of line of impact

Read moreElastic collision : In an elastic collision, the colliding particles regain their shape and

size completely after collision. i.e., no fraction of mechanical energy remains stored as

deformation potential energy in the bodies. Thus, kinetic energy of system after collision is

equal to kinetic energy of system before collision. Thus in addition to the linear momentum,

kinetic energy also remains conserved before and after collision

Read moreExamples of line of impact and collisions based on line of impact

Read moreThe coefficient of restitution is defined as the ratio of the impulses of reformation and

deformation of either body.

Read moreA particle ‘B’ moving along the dotted line collides with a rod also in state of motion as shown in the figure.

The particle B comes in contact with point C on the rod.

Read moreA pair of equal and opposite impulses act along common normal direction. Hence,

linear momentum of individual particles do change along common normal direction.

If mass of the colliding particles remain constant during collision, then we

can say that linear velocity of the individual particles change during collision in

this direction.

Read morethen the force exerted by this mass on the system has magnitude

Read moreInitially, let us suppose that the velocity of the rocket is u.

Read moreLINEAR MOMENTUM CONSERVATION IN PRESENCE OF EXTERNAL FORCE

Read moreAccording to this principle, when a body is immersed wholly or partially in a fluid, it loses its

weight which is equal to the weight of the fluid displaced by the body.

Read more