- #1
PSOA
Why is the end area of shell [tex]2\pi rdr[/tex]?
Thanks in advance.
Why is the End Area of Shell 2πrdr in the Moment of Inertia Formula?
- Thread starter PSOA
- Start date
They also congratulate each other on an award, but one of them just lost their guru badge. In summary, the end area of a shell is calculated by taking the circumference 2 times pi times r and making it thicker using dr, then integrating over r to find the total circular area. Congratulations are also exchanged for an award, but one person just lost their guru badge.
Why is the end area of shell [tex]2\pi rdr[/tex]?
Thanks in advance.
- #2
marlon
- 3,792
- 11
PSOA said:
Why is the end area of shell [tex]2\pi rdr[/tex]?
Thanks in advance.
It's the area expressed in differential form. To acquire the correct formula, you need to calculate the integral with respect to r.
Intuitively, the differential form means this : to describe an infinitesimal small area, take the circumference 2 times pi times r and make it a bit thicker, expressed by the dr. Integrating over r means that you sum up the area of all this different, very thin, circumferences to get the total circular area.
marlon
Last edited:
- #3
PSOA
Oh, I got that! Thank you marlon! I am giving my first steps over integration. And congratulations for the award!
- #4
marlon
- 3,792
- 11
What award ?PSOA said:
I just lost my guru badge to somebody else, lol.
marlon
FAQ: Why is the End Area of Shell 2πrdr in the Moment of Inertia Formula?
What is the moment of inertia formula?
The moment of inertia formula is a mathematical expression used to calculate the rotational inertia of an object. It is typically denoted as I and is equal to the mass of the object multiplied by the square of its distance from the axis of rotation.
What is the significance of the moment of inertia formula?
The moment of inertia formula is important because it helps us understand how an object's mass is distributed and how this affects its rotational motion. It allows us to predict an object's resistance to changes in its rotational speed and direction.
What is the difference between moment of inertia and mass?
Moment of inertia and mass are two different physical properties of an object. Mass is a measure of the amount of matter in an object, while moment of inertia is a measure of the object's resistance to rotational motion. While mass is a scalar quantity, moment of inertia is a tensor quantity.
How is the moment of inertia formula derived?
The moment of inertia formula can be derived using the principles of calculus and rotational dynamics. It involves integrating the mass of an object over its entire volume, taking into account the distance of each small element of mass from the axis of rotation.
What are some real-world applications of the moment of inertia formula?
The moment of inertia formula is used in a variety of fields, including engineering, physics, and mechanics. It is used in designing machines and structures that involve rotational motion, such as engines, flywheels, and gyroscopes. It is also used in sports, such as ice skating and figure skating, to calculate the moment of inertia of the athletes' bodies.