# Moment of Inertia question (dead simple)

• heyall
In summary, a thin disk with a mass of 100g, diameter of 20cm, and thickness of 2cm has a moment of inertia of 5*10^-4 kg*m2 when rotating about its central axis. The thickness does not affect the answer as long as the disk is symmetrical. The options for the answer in scientific notation are 5E-6, 1E-7, 5E5, 2E-5, and 1E4.
heyall

## Homework Statement

A thin disk is 100g.
It's diameter is 20cm.
It's thickness is 2cm.

Rotation is about the central axis (ie. perpendicular to the symmetrical plane).

## Homework Equations

I=(1/2)MR2
M is the mass
I is the moment of inertia

## The Attempt at a Solution

R = half the diameter ∴ R = 10cm

I= (.5)(.1)(.1)2
I= 0.0005 = 5*10^-4

I don't think the thickness matters as long as it is symmetrical all around.

The reason I ask is because this question is a multiple choice question for marks, but the answer I found (0.0005) wasn't listed as one of the options. Thanks!

heyall said:

## Homework Statement

A thin disk is 100g.
It's diameter is 20cm.
It's thickness is 2cm.

Rotation is about the central axis (ie. perpendicular to the symmetrical plane).

## Homework Equations

I=(1/2)MR2
M is the mass
I is the moment of inertia

## The Attempt at a Solution

R = half the diameter ∴ R = 10cm

I= (.5)(.1)(.1)2
I= 0.0005 = 5*10^-4

I don't think the thickness matters as long as it is symmetrical all around.

The reason I ask is because this question is a multiple choice question for marks, but the answer I found (0.0005) wasn't listed as one of the options. Thanks!
What are the possible options?

5E-6
1E-7
5E5
2E-5
1E4

Where the letter E indicates scientific notation.

heyall said:
5E-6
1E-7
5E5
2E-5
1E4

Where the letter E indicates scientific notation.

I agree, it's 5E-4.

I would like to clarify that the moment of inertia of a thin disk is not dependent on its thickness, as long as it is symmetrical all around. Therefore, your calculation of 0.0005 kg*m2 is correct. It is possible that the options listed for the multiple choice question are incorrect or do not take into account the correct units. I would suggest double checking your calculations and units, and if they are correct, then you can confidently choose the option closest to your calculated answer.

## What is Moment of Inertia?

Moment of Inertia is a measure of an object's resistance to changes in its rotational motion. It takes into account an object's mass, shape, and distribution of mass in relation to the axis of rotation.

## How is Moment of Inertia calculated?

Moment of Inertia can be calculated using the formula I = mr², where I is the moment of inertia, m is the mass of the object, and r is the distance of the mass from the axis of rotation. This formula is for a point mass, and for more complex objects, integrals are used to calculate the moment of inertia.

## What is the significance of Moment of Inertia?

Moment of Inertia is important in many areas of science and engineering, particularly in the study of rotational motion and dynamics. It is used to calculate the torque required to rotate an object, determine the stability of an object, and predict how an object will behave when subjected to external forces.

## How does Moment of Inertia differ from Mass?

Moment of Inertia and mass are related but distinct concepts. Mass is a measure of an object's resistance to changes in linear motion, while Moment of Inertia is a measure of an object's resistance to changes in rotational motion. Additionally, while mass is a scalar quantity, Moment of Inertia is a tensor quantity that takes into account the object's shape and distribution of mass.

## How does the Moment of Inertia change with different shapes?

The Moment of Inertia varies depending on an object's shape and distribution of mass. Objects with more mass located farther from the axis of rotation have a higher Moment of Inertia than objects with the same mass located closer to the axis of rotation. This is why long objects, like a pencil or a baseball bat, are more difficult to rotate than compact objects, like a ball or a cube, of the same mass.

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