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17 Dec 2025
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AQA A-Level Physics: Further Mechanics for Year 13
Ruth Johnson
@ruthjohnson_cbxl
1 / 3
Periodic Motion and Centripetal Force
When objects move in circles at constant speed, they're actually accelerating even though their speed stays the same. This happens because they're constantly changing direction, which means their velocity is changing.
This acceleration points towards the centre of the circle and is called centripetal acceleration. According to Newton's first law, objects naturally want to move in straight lines, so you need a force to keep them moving in circles.
The centripetal force required depends on the object's mass, speed, and the radius of the circle. You can calculate it using F = mv²/r or F = mω²r, where ω (omega) represents angular velocity - how fast the object rotates through angles.
Quick tip: Remember that centripetal force isn't a new type of force - it's just the name for whatever force (tension, friction, gravity) that's pulling the object towards the centre!
Converting between degrees and radians is essential here: 180° = π radians, so use the conversion factor π/180 when needed.
Simple Harmonic Motion (SHM)
Simple harmonic motion is everywhere - from pendulums to guitar strings to atoms vibrating in crystals. The key feature is that acceleration is always proportional to displacement but in the opposite direction: a = -ω²x.
A simple pendulum is the perfect example. When you displace it from equilibrium, it oscillates back and forth with the equation x = A cos ωt, where A is the amplitude (maximum displacement).
The displacement-time graph creates a beautiful sine or cosine curve, showing the regular pattern of oscillation. The time for one complete cycle is called the period (T).
Remember: For SHM to work with pendulums, keep the angle small (less than 10°) - otherwise the maths gets much more complicated!
The velocity changes too, following v = ±ω√. Notice how velocity is maximum at the equilibrium position and zero at maximum displacement.
Energy in Oscillating Systems
The beauty of SHM systems lies in their energy transformations. In a simple pendulum, gravitational potential energy converts to kinetic energy and back again in a continuous cycle.
For pendulums, the period formula T = 2π√ shows that longer pendulums swing more slowly. This only works for small angles because of the mathematical approximations used in deriving this formula.
Mass-spring systems work similarly but exchange kinetic energy with elastic potential energy instead of gravitational. At maximum displacement (amplitude A), all energy is potential. At equilibrium, all energy is kinetic.
The acceleration-time graph for SHM is always opposite to the displacement graph - when displacement is maximum positive, acceleration is maximum negative, showing that restoring force trying to pull the object back to equilibrium.
Energy insight: Total energy in SHM remains constant throughout the oscillation - it just keeps changing from one form to another!
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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
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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
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 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 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
AQA A-Level Physics: Further Mechanics for Year 13
Ruth Johnson
@ruthjohnson_cbxl
Ever wonder why a swinging pendulum keeps perfect time or how a car stays on a circular track? It's all about understanding periodic motion and the forces that keep objects moving in predictable patterns.
Periodic Motion and Centripetal Force
When objects move in circles at constant speed, they're actually accelerating even though their speed stays the same. This happens because they're constantly changing direction, which means their velocity is changing.
This acceleration points towards the centre of the circle and is called centripetal acceleration. According to Newton's first law, objects naturally want to move in straight lines, so you need a force to keep them moving in circles.
The centripetal force required depends on the object's mass, speed, and the radius of the circle. You can calculate it using F = mv²/r or F = mω²r, where ω (omega) represents angular velocity - how fast the object rotates through angles.
Quick tip: Remember that centripetal force isn't a new type of force - it's just the name for whatever force (tension, friction, gravity) that's pulling the object towards the centre!
Converting between degrees and radians is essential here: 180° = π radians, so use the conversion factor π/180 when needed.
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Simple Harmonic Motion (SHM)
Simple harmonic motion is everywhere - from pendulums to guitar strings to atoms vibrating in crystals. The key feature is that acceleration is always proportional to displacement but in the opposite direction: a = -ω²x.
A simple pendulum is the perfect example. When you displace it from equilibrium, it oscillates back and forth with the equation x = A cos ωt, where A is the amplitude (maximum displacement).
The displacement-time graph creates a beautiful sine or cosine curve, showing the regular pattern of oscillation. The time for one complete cycle is called the period (T).
Remember: For SHM to work with pendulums, keep the angle small (less than 10°) - otherwise the maths gets much more complicated!
The velocity changes too, following v = ±ω√. Notice how velocity is maximum at the equilibrium position and zero at maximum displacement.
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Energy in Oscillating Systems
The beauty of SHM systems lies in their energy transformations. In a simple pendulum, gravitational potential energy converts to kinetic energy and back again in a continuous cycle.
For pendulums, the period formula T = 2π√ shows that longer pendulums swing more slowly. This only works for small angles because of the mathematical approximations used in deriving this formula.
Mass-spring systems work similarly but exchange kinetic energy with elastic potential energy instead of gravitational. At maximum displacement (amplitude A), all energy is potential. At equilibrium, all energy is kinetic.
The acceleration-time graph for SHM is always opposite to the displacement graph - when displacement is maximum positive, acceleration is maximum negative, showing that restoring force trying to pull the object back to equilibrium.
Energy insight: Total energy in SHM remains constant throughout the oscillation - it just keeps changing from one form to another!
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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
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 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 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 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 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