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jackie
11/21/2025
AP Physics 1
AP Physics 1: Torque
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Understanding Torque and Center of Mass
Ever wonder why it's easier to open a door by pushing near the handle rather than near the hinges? That's torque in action! Torque measures how effectively a force causes rotation around an axis. It's calculated by multiplying force by the distance (lever arm) from the rotation axis: τ = rF sinθ. The longer the lever arm, the less force needed to create the same rotational effect.
Torque is a vector quantity with direction: positive torque creates counterclockwise rotation while negative torque causes clockwise rotation. This explains why pushing on different sides of a door creates opposite movements.
The center of gravity (or center of mass) is the point where an object's weight is effectively concentrated. For complex objects, we can calculate it using the formula xcg = /. This concept is crucial for understanding how objects balance and rotate.
💡 Real-world application: When you use a wrench to loosen a bolt, you're applying torque! The longer the wrench handle, the less force you need to apply to create the same turning effect.
Mechanical Equilibrium and Moment of Inertia
Balancing a stack of books on your head? That's mechanical equilibrium! An object is in mechanical equilibrium when three conditions are met: no acceleration in the x-direction , no acceleration in the y-direction , and no rotational acceleration (Στ = 0).
Moment of inertia (I) measures how much an object resists rotational acceleration. Think of it as the rotational equivalent of mass. It depends on both the object's mass and how that mass is distributed away from the rotation axis: I = Σmr². The formula Στ = Iα is the rotational version of Newton's Second Law .
Rotating objects possess rotational kinetic energy, calculated as KE = ½Iω². An object rolling on the floor has both translational and rotational kinetic energy. The total mechanical energy includes potential energy too, following the principle: ᵢ = f.
🔑 Key insight: The moment of inertia explains why figure skaters spin faster when they pull in their arms! By bringing their mass closer to the axis of rotation, they reduce their moment of inertia, increasing their angular velocity.
Angular Momentum
Think of angular momentum (L) as rotational momentum—it describes the "quantity of rotation" an object has. It's calculated using L = Iω or L = mvr and represents the moment of inertia in motion.
Just as force changes linear momentum, torque changes angular momentum over time: Στ = ΔL/Δt. This relationship helps us understand how rotational motion changes when torques are applied.
The most powerful principle is that angular momentum is conserved in an isolated system with no external torque (Στ = 0). This means L₁ = L₂, or I₁ω₁ = I₂ω₂. This conservation law explains many fascinating phenomena, from spinning tops to the rotation of planets.
🌟 Mind-blowing fact: Conservation of angular momentum is why cats can always land on their feet! By changing their body shape mid-fall, cats redistribute their moment of inertia while keeping their angular momentum constant.
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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
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I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
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Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. 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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. 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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Mastering Torque in AP Physics 1
Rotational motion is just as important as linear motion in physics, but with its own unique formulas and concepts. Whether it's the spinning of wheels or the swing of a door, understanding torque, angular momentum, and moment of inertia will... Show more
Understanding Torque and Center of Mass
Ever wonder why it's easier to open a door by pushing near the handle rather than near the hinges? That's torque in action! Torque measures how effectively a force causes rotation around an axis. It's calculated by multiplying force by the distance (lever arm) from the rotation axis: τ = rF sinθ. The longer the lever arm, the less force needed to create the same rotational effect.
Torque is a vector quantity with direction: positive torque creates counterclockwise rotation while negative torque causes clockwise rotation. This explains why pushing on different sides of a door creates opposite movements.
The center of gravity (or center of mass) is the point where an object's weight is effectively concentrated. For complex objects, we can calculate it using the formula xcg = /. This concept is crucial for understanding how objects balance and rotate.
💡 Real-world application: When you use a wrench to loosen a bolt, you're applying torque! The longer the wrench handle, the less force you need to apply to create the same turning effect.
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Mechanical Equilibrium and Moment of Inertia
Balancing a stack of books on your head? That's mechanical equilibrium! An object is in mechanical equilibrium when three conditions are met: no acceleration in the x-direction , no acceleration in the y-direction , and no rotational acceleration (Στ = 0).
Moment of inertia (I) measures how much an object resists rotational acceleration. Think of it as the rotational equivalent of mass. It depends on both the object's mass and how that mass is distributed away from the rotation axis: I = Σmr². The formula Στ = Iα is the rotational version of Newton's Second Law .
Rotating objects possess rotational kinetic energy, calculated as KE = ½Iω². An object rolling on the floor has both translational and rotational kinetic energy. The total mechanical energy includes potential energy too, following the principle: ᵢ = f.
🔑 Key insight: The moment of inertia explains why figure skaters spin faster when they pull in their arms! By bringing their mass closer to the axis of rotation, they reduce their moment of inertia, increasing their angular velocity.
Sign up to see the contentIt's free!
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Angular Momentum
Think of angular momentum (L) as rotational momentum—it describes the "quantity of rotation" an object has. It's calculated using L = Iω or L = mvr and represents the moment of inertia in motion.
Just as force changes linear momentum, torque changes angular momentum over time: Στ = ΔL/Δt. This relationship helps us understand how rotational motion changes when torques are applied.
The most powerful principle is that angular momentum is conserved in an isolated system with no external torque (Στ = 0). This means L₁ = L₂, or I₁ω₁ = I₂ω₂. This conservation law explains many fascinating phenomena, from spinning tops to the rotation of planets.
🌟 Mind-blowing fact: Conservation of angular momentum is why cats can always land on their feet! By changing their body shape mid-fall, cats redistribute their moment of inertia while keeping their angular momentum constant.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the 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.
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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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. 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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. 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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user