what is moment of inertia ?

MOMENT OF INERTIA 

 Translation motion 

Force  causes acceleration but mass or inertia opens it.

ROTATIONAL MOTION

Torque causes rotational accleration but M.I opposes it the role of M.I in rotational motion is same as that of mass in linner motion .

 

momentum inertia is an important property in rigid body motion. It plays the same role in rotational motion as thast of mass in linner motion .

L =IW

 

P= MV 

It is also called the rotational in inertria or it is the inability of a body to change it is state of rest or uniform rotational motion on less an external is applied .

Righd body

It is a solid body in which particles are fixed in their position and separation distance between paticles does not change due to motion .

Mathematicaly Expression for M.I 

consider a body roting about an axis. Let m1,m2,m3 ............. mn be mass of particles at perpendicular distance r1,r2, r3 .......... rn  from the axis of rotation .

Let V1,V2, ...... Vn   be the linner velocityes of paricles.  W is common angular  velcity of vall partiles as well as that of body then 

V1= r1w,  V2= r2w ...... Vn = rnw 

 

Kinetic energy of body  Ek  = sum of  kinetic energy  of all particles,

 

1/2 M1V1+ 1/2 M2V2+ ..........  + 1/2 Mn vn

= 1/2 M1R1 R1W1 + 1/2 M2R2R2 W2 +....+1/2 Mn Rn w2 

=1/2 (M1 R1R1 +....... + MnRn Rn ) w2

E k =  1/2 IWW

Where I= M1 R1*R1+M2r2*r2 ............... + Mnrn*rn = M.I of mass particles with squre of perpendicular distance form their axis of roation 

If the body constants single  particles then M.I 

I=mrr