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UKRevisionResources
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Ever wondered how objects move and what forces act on... Show more







Physics would be impossible without making smart assumptions about real objects! When you're solving mechanics problems, you'll treat complex objects as simplified models that are much easier to work with.
A particle has negligible dimensions - imagine all its mass squeezed into a single point. This lets you ignore awkward rotational forces and focus on the main motion. Rods have their mass concentrated along a line, whilst laminas spread their mass across a flat surface like a sheet of paper.
Light objects have virtually no mass, which creates some brilliant shortcuts. Light strings have the same tension throughout their length, and light pulleys don't affect the tension passing over them. Inextensible strings don't stretch, meaning connected objects always have the same acceleration.
Key Insight: These assumptions aren't "cheating" - they're essential tools that help you solve real problems without getting bogged down in unnecessary complications!
Surface types matter hugely in mechanics. Smooth surfaces produce no friction (think ice), whilst rough surfaces create friction that opposes motion. Most exam questions will clearly state which type you're dealing with.

Forces have both magnitude and direction, making them vectors that need special treatment. You'll constantly switch between vector notation and finding magnitudes using Pythagoras' theorem.
Speed versus velocity trips up loads of students! Speed is always positive (it's a scalar), whilst velocity can be positive or negative depending on direction. Distance is the magnitude of displacement, and speed is the magnitude of velocity.
Force diagrams are absolutely crucial - always draw them! You'll see normal reactions (perpendicular to surfaces), tension (along strings), friction (opposing motion), weight (always downward), and air resistance (opposing motion through air).
Essential Skill: Master the relationship |V| = √ for finding vector magnitudes - you'll use it constantly throughout mechanics!
Converting between different units before calculating is non-negotiable. Metres, seconds, kilograms, and metres per second squared are your standard SI units. Most exam disasters happen because someone forgot to convert!

Calculus is your best mate when acceleration isn't constant! You'll need to master the relationship between displacement, velocity, and acceleration using differentiation and integration.
Differentiation gets you from displacement to velocity , and from velocity to acceleration . Going backwards, integration takes you from acceleration to velocity (∫a dt), and from velocity to displacement (∫v dt). Think of it as climbing up and down a mathematical ladder.
To find maximum or minimum values, differentiate the appropriate equation and set it equal to zero. You'll often get a quadratic equation to solve. Remember to check your answers against any time constraints given in the question!
Pro Tip: Always substitute your final time value back into the original displacement equation to find the actual maximum or minimum position.
The worked example shows this perfectly - differentiating the displacement equation, setting equal to zero, solving the quadratic, then checking the time constraint (0 ≤ t ≤ 3). Only keep solutions that fit within the given time range.

Newton's three laws govern everything that moves! The first law says objects keep doing what they're doing unless forces act on them. The second law gives you F = ma - the most important equation in mechanics. The third law means every action has an equal and opposite reaction.
Resultant force determines acceleration direction. When forces are balanced (equilibrium), the resultant force is zero and there's no acceleration. For constant velocity, forces must be perfectly balanced even though the object is moving.
Connected particles need separate F = ma equations for each object, then solve simultaneously. Always choose the positive direction as the direction of acceleration - it makes calculations much cleaner.
Game Changer: List out s, u, v, a, t values at the start of every problem. This simple habit prevents most calculation errors!
The SUVAT equations work brilliantly for constant acceleration problems. Which equation you choose depends on which variable you don't know. No time? Use v² = u² + 2as. No final velocity? Use s = ut + ½at².

Graphs tell the complete story of motion! On displacement-time graphs, the gradient gives velocity, whilst curved lines show changing velocity. Horizontal lines mean the object is stationary.
Velocity-time graphs have gradient equal to acceleration, and the area under the curve gives displacement. Lines below the time axis indicate motion in the opposite direction - don't forget this catches many students out!
The five SUVAT equations handle all constant acceleration problems. Choose your equation based on which quantity you don't have: no time means use v² = u² + 2as, no final velocity means use s = ut + ½at².
Gravity Game-Changer: You can choose up or down as positive, but gravity always acts downward at 9.8 ms⁻². Stay consistent with your choice throughout each problem!
Vertical motion problems use gravity as constant downward acceleration. Whether you're dealing with projectiles, dropped objects, or things thrown upward, g = 9.8 ms⁻² unless stated otherwise. Maximum height occurs when velocity equals zero.

Two-dimensional motion uses vector addition for forces and accelerations. You'll often need to resolve forces into horizontal and vertical components using F = ma in each direction separately.
Pulleys create fascinating problems! The tension is the same throughout a light string passing over a smooth pulley. Set up separate F = ma equations for each hanging mass, then solve simultaneously to find the common acceleration.
For variable acceleration problems, integration becomes your main tool. Finding displacement when given acceleration? Integrate twice. Looking for when an object returns to its starting position? Set the displacement equation equal to zero.
Top Strategy: Always take the positive direction as the direction of acceleration - it eliminates most sign errors and confusion!
Connected particles must be treated individually unless they're moving together in the same straight line. Use R(→), R(↑) notation to show which direction you're resolving forces in. This keeps your working crystal clear.
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
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 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
UKRevisionResources
@ukrevisionresources
Ever wondered how objects move and what forces act on them? Mechanics is the branch of physics that explains everything from a ball flying through the air to cars braking on different surfaces. You'll learn to model real-world situations using... Show more

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Physics would be impossible without making smart assumptions about real objects! When you're solving mechanics problems, you'll treat complex objects as simplified models that are much easier to work with.
A particle has negligible dimensions - imagine all its mass squeezed into a single point. This lets you ignore awkward rotational forces and focus on the main motion. Rods have their mass concentrated along a line, whilst laminas spread their mass across a flat surface like a sheet of paper.
Light objects have virtually no mass, which creates some brilliant shortcuts. Light strings have the same tension throughout their length, and light pulleys don't affect the tension passing over them. Inextensible strings don't stretch, meaning connected objects always have the same acceleration.
Key Insight: These assumptions aren't "cheating" - they're essential tools that help you solve real problems without getting bogged down in unnecessary complications!
Surface types matter hugely in mechanics. Smooth surfaces produce no friction (think ice), whilst rough surfaces create friction that opposes motion. Most exam questions will clearly state which type you're dealing with.

Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Forces have both magnitude and direction, making them vectors that need special treatment. You'll constantly switch between vector notation and finding magnitudes using Pythagoras' theorem.
Speed versus velocity trips up loads of students! Speed is always positive (it's a scalar), whilst velocity can be positive or negative depending on direction. Distance is the magnitude of displacement, and speed is the magnitude of velocity.
Force diagrams are absolutely crucial - always draw them! You'll see normal reactions (perpendicular to surfaces), tension (along strings), friction (opposing motion), weight (always downward), and air resistance (opposing motion through air).
Essential Skill: Master the relationship |V| = √ for finding vector magnitudes - you'll use it constantly throughout mechanics!
Converting between different units before calculating is non-negotiable. Metres, seconds, kilograms, and metres per second squared are your standard SI units. Most exam disasters happen because someone forgot to convert!

Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Calculus is your best mate when acceleration isn't constant! You'll need to master the relationship between displacement, velocity, and acceleration using differentiation and integration.
Differentiation gets you from displacement to velocity , and from velocity to acceleration . Going backwards, integration takes you from acceleration to velocity (∫a dt), and from velocity to displacement (∫v dt). Think of it as climbing up and down a mathematical ladder.
To find maximum or minimum values, differentiate the appropriate equation and set it equal to zero. You'll often get a quadratic equation to solve. Remember to check your answers against any time constraints given in the question!
Pro Tip: Always substitute your final time value back into the original displacement equation to find the actual maximum or minimum position.
The worked example shows this perfectly - differentiating the displacement equation, setting equal to zero, solving the quadratic, then checking the time constraint (0 ≤ t ≤ 3). Only keep solutions that fit within the given time range.

Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Newton's three laws govern everything that moves! The first law says objects keep doing what they're doing unless forces act on them. The second law gives you F = ma - the most important equation in mechanics. The third law means every action has an equal and opposite reaction.
Resultant force determines acceleration direction. When forces are balanced (equilibrium), the resultant force is zero and there's no acceleration. For constant velocity, forces must be perfectly balanced even though the object is moving.
Connected particles need separate F = ma equations for each object, then solve simultaneously. Always choose the positive direction as the direction of acceleration - it makes calculations much cleaner.
Game Changer: List out s, u, v, a, t values at the start of every problem. This simple habit prevents most calculation errors!
The SUVAT equations work brilliantly for constant acceleration problems. Which equation you choose depends on which variable you don't know. No time? Use v² = u² + 2as. No final velocity? Use s = ut + ½at².

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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Graphs tell the complete story of motion! On displacement-time graphs, the gradient gives velocity, whilst curved lines show changing velocity. Horizontal lines mean the object is stationary.
Velocity-time graphs have gradient equal to acceleration, and the area under the curve gives displacement. Lines below the time axis indicate motion in the opposite direction - don't forget this catches many students out!
The five SUVAT equations handle all constant acceleration problems. Choose your equation based on which quantity you don't have: no time means use v² = u² + 2as, no final velocity means use s = ut + ½at².
Gravity Game-Changer: You can choose up or down as positive, but gravity always acts downward at 9.8 ms⁻². Stay consistent with your choice throughout each problem!
Vertical motion problems use gravity as constant downward acceleration. Whether you're dealing with projectiles, dropped objects, or things thrown upward, g = 9.8 ms⁻² unless stated otherwise. Maximum height occurs when velocity equals zero.

Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Two-dimensional motion uses vector addition for forces and accelerations. You'll often need to resolve forces into horizontal and vertical components using F = ma in each direction separately.
Pulleys create fascinating problems! The tension is the same throughout a light string passing over a smooth pulley. Set up separate F = ma equations for each hanging mass, then solve simultaneously to find the common acceleration.
For variable acceleration problems, integration becomes your main tool. Finding displacement when given acceleration? Integrate twice. Looking for when an object returns to its starting position? Set the displacement equation equal to zero.
Top Strategy: Always take the positive direction as the direction of acceleration - it eliminates most sign errors and confusion!
Connected particles must be treated individually unless they're moving together in the same straight line. Use R(→), R(↑) notation to show which direction you're resolving forces in. This keeps your working crystal clear.
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.
You can download the app from Google Play Store and Apple App Store.
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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Comprehensive Year 1 Mechanics study material covering key concepts such as uniform motion, acceleration, Newton's Laws of Motion, kinematic equations, and free-body diagrams. Ideal for A-level Edexcel students, this resource provides essential insights into motion, forces, and mechanical systems, ensuring a solid foundation in Newtonian Mechanics.
Explore key concepts in kinematics, including average velocity, displacement, and acceleration. This summary covers essential calculations and examples from the first lesson of A-level Mechanics, focusing on displacement-time graphs and their implications in motion analysis. Ideal for Edexcel A-level Maths students.
Explore key concepts of projectile motion including final velocity, time of flight, and trajectory analysis. This comprehensive summary covers both vertical and horizontal components, providing essential calculations and examples for A Level Maths (AQA). Perfect for mastering mechanics in physics.
Explore detailed worked solutions for the A-Level Maths Paper 1 (2022). This resource covers key concepts such as differentiation, exponential functions, trigonometric equations, and area calculations, providing step-by-step explanations for each question. Ideal for students preparing for exams.
Explore the principles of kinematics in two-dimensional motion, including key concepts such as displacement, velocity, acceleration, and the kinematic equations. This summary provides essential insights for A Level Maths students, focusing on constant acceleration and relative motion between particles. Ideal for exam preparation and understanding motion dynamics.
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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