Ever wondered why it's easier to open a door by... Show more
Physics
English Literature
Biology
SociologySign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
33
•
23 Jan 2026
•
Physics Module 1: Chapter 2 Overview
F
Felicia Kennedy
@feliciathegoat_
1 / 10
Module Introduction
This General Physics module dives into one of the most practical areas of mechanics you'll encounter. While you've already mastered forces in equilibrium, now you're stepping up to tackle parallel non-concurrent forces – forces that don't meet at a single point but can still create fascinating effects.
You'll master three key skills that'll serve you well in exams and real life. First, calculating moment of inertia for both single objects and complex systems. Second, working out torque magnitude and direction using cross products. Finally, describing rotational equilibrium using vectors.
Key Insight: Unlike the simple force equilibrium you've studied before, rotational systems introduce the exciting possibility of objects that want to spin even when forces are balanced!
Think of this as your gateway to understanding why engineers design car wheels the way they do, or how gymnasts control their spinning speed during routines.
Finding the Center of Gravity
Understanding center of gravity is absolutely crucial before diving into rotational motion. It's that special point where all of an object's weight can be considered to act from – like the perfect balance point.
For regular shapes like circles or rectangles, finding the center of gravity is straightforward – it's simply the geometric center. However, irregular shapes require a clever technique using a plumb line and pin to trace intersecting lines from different hanging points.
The practical activity with cardboard shapes demonstrates why multiple measurement lines are essential. Each line represents the direction of gravitational force from that hanging position, and their intersection reveals the true center of gravity.
Pro Tip: The center of gravity isn't always at the geometric center for irregular objects – this principle is crucial for understanding vehicle stability and building design!
This concept becomes your foundation for analyzing how objects will behave when forces try to make them rotate.
Understanding Torque
Torque is simply the measure of how much a force wants to make something rotate – think of it as "rotational force." When you apply a perpendicular force to a lever arm, you create this turning effect that can cause clockwise or counterclockwise rotation.
The basic torque formula is beautifully simple: τ = F × la, where τ is torque, F is the applied force, and la is the lever arm distance from the pivot point. When forces act at angles, you'll need the perpendicular component: τ = (F cos θ) × la.
Direction matters enormously in torque calculations. Clockwise rotations produce negative torque, while counterclockwise rotations give positive torque. This sign convention helps you determine whether competing torques will cancel each other out or add together.
Real-World Connection: Every time you use a wrench, you're applying torque principles – longer handles give greater turning power for the same applied force!
The examples show straightforward calculations: a 10 N force at 2 m creates 20 N⋅m of torque, demonstrating how distance dramatically amplifies rotational effect.
Moment of Inertia Fundamentals
Moment of inertia is an object's resistance to changes in rotational motion – essentially the rotational equivalent of mass for linear motion. Just as heavier objects resist changes in straight-line motion, objects with larger moments of inertia resist changes in spinning motion.
For a single point mass, the formula is elegantly simple: I = mr². This reveals why distance from the rotation axis matters so much – since radius is squared, moving twice as far from the center quadruples the moment of inertia.
When dealing with multiple particles, you simply add up each contribution: I = Σ mᵢrᵢ². Each particle contributes based on both its mass and its distance from the rotation axis, squared.
Key Insight: Figure skaters use moment of inertia when they pull their arms in to spin faster – reducing their radius decreases their moment of inertia, so they speed up to conserve angular momentum!
The worked examples demonstrate practical calculations, showing how to convert units properly and handle multi-particle systems with precision.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content: Newton's Laws of Motion
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Physics Module 1: Chapter 2 Overview
F
Felicia Kennedy
@feliciathegoat_
Ever wondered why it's easier to open a door by pushing near the handle rather than close to the hinges? Welcome to the fascinating world of torque and moment of inertia– the physics behind rotational motion that explains everything... Show more
Module Introduction
This General Physics module dives into one of the most practical areas of mechanics you'll encounter. While you've already mastered forces in equilibrium, now you're stepping up to tackle parallel non-concurrent forces – forces that don't meet at a single point but can still create fascinating effects.
You'll master three key skills that'll serve you well in exams and real life. First, calculating moment of inertia for both single objects and complex systems. Second, working out torque magnitude and direction using cross products. Finally, describing rotational equilibrium using vectors.
Key Insight: Unlike the simple force equilibrium you've studied before, rotational systems introduce the exciting possibility of objects that want to spin even when forces are balanced!
Think of this as your gateway to understanding why engineers design car wheels the way they do, or how gymnasts control their spinning speed during routines.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Finding the Center of Gravity
Understanding center of gravity is absolutely crucial before diving into rotational motion. It's that special point where all of an object's weight can be considered to act from – like the perfect balance point.
For regular shapes like circles or rectangles, finding the center of gravity is straightforward – it's simply the geometric center. However, irregular shapes require a clever technique using a plumb line and pin to trace intersecting lines from different hanging points.
The practical activity with cardboard shapes demonstrates why multiple measurement lines are essential. Each line represents the direction of gravitational force from that hanging position, and their intersection reveals the true center of gravity.
Pro Tip: The center of gravity isn't always at the geometric center for irregular objects – this principle is crucial for understanding vehicle stability and building design!
This concept becomes your foundation for analyzing how objects will behave when forces try to make them rotate.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Understanding Torque
Torque is simply the measure of how much a force wants to make something rotate – think of it as "rotational force." When you apply a perpendicular force to a lever arm, you create this turning effect that can cause clockwise or counterclockwise rotation.
The basic torque formula is beautifully simple: τ = F × la, where τ is torque, F is the applied force, and la is the lever arm distance from the pivot point. When forces act at angles, you'll need the perpendicular component: τ = (F cos θ) × la.
Direction matters enormously in torque calculations. Clockwise rotations produce negative torque, while counterclockwise rotations give positive torque. This sign convention helps you determine whether competing torques will cancel each other out or add together.
Real-World Connection: Every time you use a wrench, you're applying torque principles – longer handles give greater turning power for the same applied force!
The examples show straightforward calculations: a 10 N force at 2 m creates 20 N⋅m of torque, demonstrating how distance dramatically amplifies rotational effect.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Moment of Inertia Fundamentals
Moment of inertia is an object's resistance to changes in rotational motion – essentially the rotational equivalent of mass for linear motion. Just as heavier objects resist changes in straight-line motion, objects with larger moments of inertia resist changes in spinning motion.
For a single point mass, the formula is elegantly simple: I = mr². This reveals why distance from the rotation axis matters so much – since radius is squared, moving twice as far from the center quadruples the moment of inertia.
When dealing with multiple particles, you simply add up each contribution: I = Σ mᵢrᵢ². Each particle contributes based on both its mass and its distance from the rotation axis, squared.
Key Insight: Figure skaters use moment of inertia when they pull their arms in to spin faster – reducing their radius decreases their moment of inertia, so they speed up to conserve angular momentum!
The worked examples demonstrate practical calculations, showing how to convert units properly and handle multi-particle systems with precision.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
0
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Mock Exam
Quiz
Flashcards
Essay
Most popular content: Newton's Laws of Motion
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user