# Rotational moment of inertia in Kg*m^2

• gesk0015
In summary, the conversation discusses estimating the total rotational moment of inertia in kg*m^2 of all the motors and generators in the Eastern United States. The attempt at a solution includes using a website to estimate the generation capacity of the Eastern U.S., converting kilowatts to joules, and acknowledging the need for assumptions about the size of the generators to accurately calculate the moment of inertia. The conversation also mentions the importance of correctly spelling and capitalizing units, and provides a resource for the correct spelling of unit symbols.
gesk0015

## Homework Statement

Estimate the total rotational moment of inertia in Kg*m^2, of all the motors and generators in the Eastern United States.

## Homework Equations

No other information was provided.

## The Attempt at a Solution

First off I went to the following website to estimate the generation capacity of the Eastern U.S.

http://www.eia.doe.gov/cneaf/electricity/epm/table1_6_a.html

I came up with a total of 2.1673e8 MWh for the Eastern U.S.
=2.1673e11 KWh

I know that 1 KW=3600 Joules.

so from this I get a total of 7.80228e14 Joules

From here I am at a loss at how to convert this to rotational moment of Inertia( Kg*m^2)

Moment of inertia is a geometrical property, and is not related to performance. You will have to do some assumptions about the size of the generators and extrapolate polar moments of inertia from that assumption. Good luck.

gesk0015: You must list relevant equations yourself. We are not allowed to list the relevant equations for you.

By the way, you misspelled several units. E.g., K means kelvin; k means kilo. Always use correct capitalization of units. See NIST for the correct spelling of any unit symbol. Here is the correct spelling of all the units you misspelled: kg, kW, kW*h, MW*h, joule. You also have an incorrect conversion listed.

## 1. What is rotational moment of inertia?

Rotational moment of inertia, also known as moment of inertia or angular mass, is a measure of an object's resistance to changes in its rotational motion. It is similar to mass in linear motion, but instead measures an object's resistance to rotational acceleration.

## 2. How is rotational moment of inertia calculated?

The rotational moment of inertia is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. In equation form, it can be written as I = mr^2, where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation.

## 3. How does the shape of an object affect its rotational moment of inertia?

The shape of an object has a significant impact on its rotational moment of inertia. Objects with a larger mass and/or a larger distance from the axis of rotation will have a higher moment of inertia, while objects with a smaller mass and/or a smaller distance from the axis of rotation will have a lower moment of inertia. Additionally, objects with a more distributed mass (such as a ring or a disk) will have a higher moment of inertia compared to objects with a more centralized mass (such as a sphere).

## 4. Why is rotational moment of inertia an important concept in physics?

Rotational moment of inertia is an important concept in physics because it helps us understand how objects behave when they are rotating. It is a crucial factor in understanding and predicting the motion of objects, such as in the case of a spinning top or a rotating planet. It also plays a key role in the laws of conservation of angular momentum, which is a fundamental principle in physics.

## 5. How can rotational moment of inertia be applied in real life?

Rotational moment of inertia has numerous applications in everyday life. It is used in the design and engineering of various objects, such as wheels, gears, and flywheels, to ensure they rotate smoothly and efficiently. It is also a crucial concept in sports, particularly in activities that involve rotation, such as gymnastics, figure skating, and diving. Additionally, the rotational moment of inertia is used in the design of vehicles, such as cars and planes, to ensure they are stable and easy to control.

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