###### Asked in PhysicsLakes and RiversDams

Physics

Lakes and Rivers

Dams

# What is the moment of inertia of a disk of radius 12cm and mass 2.4kg from whose edge a circular portion of radius 3cm has been cut off?

## Answer

###### Wiki User

###### April 02, 2010 3:08PM

It can be done, but it would require taking an integral for the moment of inertia of each particle of the disc... something i don't have the time to do right now ^^;

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### Moment of inertia of a semi circular wire of mass m?

If we are considering the semi circular wire of mass m to have a
relatively small cross sectional radius, r compared to radius of
the semi circular arc, R
And that we are considering the semi circular wire to lie in a
xy plane. The mass moment of inertia taken about the z-axis
(perpendicular to the plane) located at the cg position will
be.
Izz=m*(R^2)*(PI-(4/PI))/PI
I did a check of this calculation with the way Catia calculated
the same property. And the difference was found to be 0.03% When
using the following geometry.
density=0.000001kgmm^3
Semi circular wire Radius R =60mm
cross sectional radius of wire = 1mm
results from Catia
V=592.176mm^3
m=0.000592176kg
Izz=1.268159kgmm^2
hand calculated results
V=592.176mm^3
m=0.000592176kg
Izz=1.267835kgmm^2
% difference [((1.268159)-(1.267835))/(1.267835)]*100=0.03%
Please carry out a check on the Izz calc. I determined it from
1st principles, so I may of made a mistake

###### Asked in Physics

### Why does the coasting rotating system slow as water drips into the beaker?

Ans : By the formula of moment of inertia ,
I=mr2 (2=square)
As by the formula it is clear that the moment of inertia depends
on the mass and the radius of a particular body , so as the mass
increases moment of inertia will considerably increase , So as the
water drips into the beaker the mass of the beaker will
increase
By the law of conservation of angular momentum
Moment of inertia is inversely proportional to the angular
velocity ( omega ) , Since in the above case of coasting rotating
system moment of inertia is increased so the angular velocity
(omega) will also decrease and hence the coasting rotating system
will now rotate slowly as compared to its rotation before dripping
water !

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