matter physics

7/26/2019 Matter physics

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Matter anything which have mass and occupy space (i.e. have volume) and

which can be felt i.e. solid, liquid and gases.

Particle / point obect in!nitely small part of matter for which we can ignore si"e

(i.e. volume can be assumed to #).

$ystem of particle when study of motion of !nite no. of particle is donetogether they are called system of particles.

%ody &ragment of matter which occupy limited area (i.e. volume is !'ed) and

which has shape is called body. (in simple solids) t is group of in!nite particles.

$mooth body body which doesnt oppose relative motion of other bodies on its

surface. (friction*#)

+igid body body whose particles have no relative motion to each other.

o-body in nature is either perfectly smooth or perfectly rigid.

+eal bodies deform under inuence of forces but in most casesdeformation is negligible so we can assume then rigid body

is used for !nite change, is used for in!nitely small changes. &or

calculus they are used interchangeably but when we tal about dx and

compare it without any limit with change in other quantity then

should be used. f we can !nd absolute values for any variable then for

in!nitely small change (i.e. for change tends to #) we use dx but if we

cant measure absolute value and only can measure in!nitely small

di0erences in value of variable then we usex

. %est e'ample isthermodynamic !rst eq.

till now we studied for point particle motion only and applied result tobody of !nite si"e assuming that their motion can be described as motion

of particle. ow we will study the motion of e'tended bodies (simply body

or rigid body) beyond this limitation.1. Diferent kind o motion a rigid body can have-

a) Pure translational -at any instant of time every particle of the body

has the same velocity. 1'- rectangular bloc sliding down an inclined

planeb) Pure rotational -in rotation of a rigid body about a !'ed a'is, every

particle of the body moves in a circle, which lies in a planeperpendicular to the a'is and has its centre on the a'is. 1'- celling fan.

Particles on a'is remain stationary.c) Precession (also a type o

rotational)-in rotation of a rigid body

if a'is is not !'ed but one point of a'is

is !'ed i.e. no translational motion

taing place. 1'- spinning top (point of

contact of the top with ground is !'ed

i.e. pivoted) a'is of such a spinning

top moves around the vertical through

its point of contact with the ground,sweeping out a cone.


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2ther e'- oscillating table fand) Combination o translational and rotational -3he motion of a rigid

body which is not pivoted or !'ed in some way is either a pure

translation or a combination of translation and rotation. 1'- cylindrical

obect rolling down an inclined plane.

. Centre o mass a) !or system o particles - tae the line

oining the two particles m4 and m5to be

the '- a'is and the distances of the two

particles be '4and '5respectively from

some origin 2. 3hen position of centre of

mass of system 6 isX=

m1x

1+m

2x

2

m1+m2

"pecial case -3hus, for two particles of equal mass the centre of

mass lies e'actly midway between them. X=

x1+x

2

2

b) !or system o n particles in 1-D -

X=m

1x

1+m

2x

2++mnxn

m1+m

2++mn

=i=1

n

mixi

i=1

n

mi

=i=1

n

mix i

M

c) !or system o n particles in -D (plane) -

X=

i=1

n

mixi

M Y=

i=1

n

miy i

M

"pecial case -3hus, for three particles we have a plane which can

have them, if they are of equal mass the centre of mass lies on

centroid of the triangle formed by the particles.

X=x

1+x

2+x

3

2Y=

y1+y

2+y

3

2

d) !or system o n particles in #-D -

X=

i=1

n

mixi

M Y=

i=1

n

miy i

M Z=

i=1

n

mizi

M

we canwrite these combinedly as positionvector form as R=i=1

n

mi ri

Mf the

origin of the frame of reference (the coordinate system) is chosen to be

the centre of mass then i=1

n

mi ri=0

e) !or rigid body- i.e.n

we can treat the body as a continuousdistribution of mass.


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we assume rigid body of mass M is made of 7 element of equal

mass dm (so we have equal miand continuous distribution i.e. distance

between consecutive dm be same)

X=limm 0

i=1

n

mixi

M =

xdmM

Y=

ydmM

Z=

zdmM

3he centre of mass is not the point at which a plane separates thedistribution of mass into two equal halves. 6entre of mass is lie the pivot

point which balances seesaw of masses about itself, with respect to the

torques produced by them.

1'- for uniform road - X=xdm

M =0

x !(M

dx)

M =

2

matter physics

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