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Moment of Inertia Calculator

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The inertia of a particle or larger object is a measure of its resistance to move. When a body can be modeled as a particle, its mass determines its inertia. For a larger body which is rotating about a fixed axis the particle model is no longer appropriate and its reluctance to move is determined by a quantity called its moment of inertia. It is denoted as I and SI unit is kg$m^{2}$.

The formula to calculate the moment of inertia is,
$I = MD^{2}$

Where M is the mass
           D is the distance from the axis of rotation
 

Steps

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Step 1: Note down the given parameters from the question.
Step 2: Plug these given quantity in $I = MD^{2}$
Step 3: Calculate the unknown quantity

Problems

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The problems of Moment of Inertia are given below:

Solved Examples

Question 1: The mass of a bob is 10g and the distance between bob and axis of rotation is 35cm. Calculate its moment of inertia?

Solution:
 
Given measures are,
m = 10g = 0.01kg
r = 35cm = 0.35m
The formula to calculate the moment of inertia is,
$I = MD^{2}$

I = 0.01$\times0.35^{2}$ = 0.001225 kg$m^{2}$

 

Question 2: Mass and distance between an object and axis of rotation are given as 5kg and 10m respectively. Calculate its moment of inertia?
Solution:
 
Given measures are,
m = 5kg
r = 10m
The formula to calculate the moment of inertia is,
$I = MD^{2}$

I = 5$\times10^{2}$ = 500 kg$m^{2}$