Skip to player
Skip to main content
Skip to footer
Search
Connect
Watch fullscreen
Like
Comments
Bookmark
Share
Add to Playlist
Report
Moment of Inertia of a Point Particle
Rebiaz Studio
Follow
8/20/2024
A point particle, a particle that has mass but no size, rotates about a fixed axis. How do we calculate the moment of inertia of a point particle.
Category
📚
Learning
Transcript
Display full video transcript
00:00
An object rotates through a specific axis.
00:07
In the previous series, we were familiar with the term moment of inertia,
00:11
which is nothing but a measure of an object's ability to maintain its angular velocity.
00:19
This quantity is often symbolized as big I. I is for inertia.
00:24
The moment of inertia is proportional to the mass of the object.
00:33
The moment of inertia is proportional to the radius of the object relative to the axis.
00:39
Mathematically, the moment of inertia can be calculated through the equation I equals m r
00:43
squared. This equation is valid for point particles. An object that has mass but no size.
00:54
To understand this equation further, in a three-dimensional Cartesian coordinate system,
01:05
there are point particles with coordinates r sub x, r sub y, r sub z, where the r sub z value is zero.
01:14
We will calculate the value of the moment of inertia about three axes, the x-axis, y-axis,
01:20
and z-axis. So, we will duplicate this system into three.
01:31
In the first system, the particles will rotate about the x-axis.
01:36
This means that the axis is the x-axis.
01:41
We should be able to imagine this particle rotating about the x-axis.
01:45
Even though the intersection point on the x-axis is r sub x,
01:48
the distance from the point to the axis is r sub y.
01:54
Thus, the value of the moment of inertia on the x-axis, I sub x is equal to m r sub x squared.
02:03
In the second system, the particles will rotate about the y-axis.
02:09
This means the axis is the y-axis.
02:12
This means the axis is the y-axis.
02:17
Now the distance of the point to the axis is r sub x.
02:22
Thus, the value of the moment of inertia on the y-axis, I sub y is equal to m r sub y squared.
02:32
In the third system, the particles will rotate about the z-axis.
02:37
This means that the axis is the z-axis.
02:42
The distance from the point to the axis is the length of the line perpendicular to the axis leading to the point particle.
02:50
Using the Pythagorean theorem, the length of this line is the root of r sub x squared, plus r sub y squared.
02:59
Thus, the value of the moment of inertia on the z-axis, I sub z is equal to m,
03:04
multiplied by r sub x squared plus r sub y squared.
03:12
From here, we can see that the same particle can have several values of moment of inertia depending on its axis.
03:23
Thank you for watching this video.
03:26
And, don't forget to watch the next video.
Recommended
2:59
|
Up next
Moment of Inertia of Discrete Particles
Rebiaz Studio
8/21/2024
2:51
Moment of Inertia of Rigid Body
Rebiaz Studio
8/22/2024
3:28
Moment of Inertia Concept
Rebiaz Studio
8/19/2024
2:54
Impulse -02- Particle Velocity From Instantaneous Force
Rebiaz Studio
10/19/2024
10:38
Moment of Inertia & Moment of Inertia for a rigid Body
Punjab Group Of Colleges
1/16/2016
3:31
The Angular Frequency of Simple Pendulum on Simple Harmonic Motion | Oscillation | 11th Class Physics
Rebiaz Studio
10/1/2023
16:36
Angular Momentum &Law of conservation of Angular Momentum
Punjab Group Of Colleges
1/18/2016
2:02
Problem No 5.3 : A body of moment of inertia .......
Punjab Group Of Colleges
1/20/2016
1:03:20
Rotation Motion, Moment Of Inertia, IIT-JEE/NEET #neet #jeemains #momentofinertia #rotationalmotion
sun ray
6/23/2024
4:00
System of Particles and Rotational Motion
Extraminds
8/27/2018
3:06
Newton's laws of Rotation
Rebiaz Studio
8/28/2024
2:06
Rotational Kinematics -03- Centripetal Acceleration
Rebiaz Studio
10/29/2024
0:46
The product of the rotational inertia about an axis and the angular velocity of a body rotating about this axis is called
Physics with Akhtiar Ali Bullo
2/20/2025
2:29
Laws of Motion -03- Moment Of A Force
Rebiaz Studio
9/21/2024
0:25
Physics Olympiad #001 [Kinematics Of Translation Motion]
Rebiaz Studio
4/24/2024
1:52
Rotational Kinematics -01- Tangential Acceleration
Rebiaz Studio
10/25/2024
2:04
Rotational Kinematics -02- Angular Acceleration
Rebiaz Studio
10/27/2024
10:55
Centripetal Force
Punjab Group Of Colleges
1/16/2016
2:43
Parabolic Motion -02- Coordinates of Particles in Projectile Motion
Rebiaz Studio
9/26/2024
1:06
For a npn transistor the p-type crystal only acts as a
Physics with Akhtiar Ali Bullo
3 days ago
0:29
What is kinetic energy?
Physics with Akhtiar Ali Bullo
3/15/2025
2:07
Prove that one erg is equal to 10 power -7 joule_-_ prove that 1 erg=10-7J
Physics with Akhtiar Ali Bullo
11/8/2024
2:58
Drawbacks of Rutherford Model - Structure Of Atom
Rebiaz Studio
4/21/2025
3:14
Atomic Number and Mass Number - Structure Of Atom
Rebiaz Studio
4/15/2025
2:02
Isotope Concept - Structure Of Atom
Rebiaz Studio
4/14/2025