# Urgent physics angular motion problem

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Two children of mass m are pushing a roundabout at a playground to speed it up. They are each pushing with a force F, tangentially to the edge of the circular roundabout. This is causing an angular acceleration of the roundabout of α.

The roundabout has a moment of inertia about an axis through its centre of I=Mr22, where Mis t he mass of the roundabout and r is its radius. The radius of the roundabout is much bigger than the size of the children. Assume there is no friction between the roundabout and its axle, and ignore air resistance.

One of the children stops pushing and jumps onto the very edge of the roundabout.

In terms of F, m, M and r, what force must the other child now push with to maintain the same angular acceleration of the roundabout?

The roundabout has a moment of inertia about an axis through its centre of I=Mr22, where Mis t he mass of the roundabout and r is its radius. The radius of the roundabout is much bigger than the size of the children. Assume there is no friction between the roundabout and its axle, and ignore air resistance.

One of the children stops pushing and jumps onto the very edge of the roundabout.

In terms of F, m, M and r, what force must the other child now push with to maintain the same angular acceleration of the roundabout?

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#2

(Original post by

Two children of mass m are pushing a roundabout at a playground to speed it up. They are each pushing with a force F, tangentially to the edge of the circular roundabout. This is causing an angular acceleration of the roundabout of α.

The roundabout has a moment of inertia about an axis through its centre of I=Mr22, where Mis t he mass of the roundabout and r is its radius. The radius of the roundabout is much bigger than the size of the children. Assume there is no friction between the roundabout and its axle, and ignore air resistance.

One of the children stops pushing and jumps onto the very edge of the roundabout.

In terms of F, m, M and r, what force must the other child now push with to maintain the same angular acceleration of the roundabout?

**student273**)Two children of mass m are pushing a roundabout at a playground to speed it up. They are each pushing with a force F, tangentially to the edge of the circular roundabout. This is causing an angular acceleration of the roundabout of α.

The roundabout has a moment of inertia about an axis through its centre of I=Mr22, where Mis t he mass of the roundabout and r is its radius. The radius of the roundabout is much bigger than the size of the children. Assume there is no friction between the roundabout and its axle, and ignore air resistance.

One of the children stops pushing and jumps onto the very edge of the roundabout.

In terms of F, m, M and r, what force must the other child now push with to maintain the same angular acceleration of the roundabout?

To start with, consider the forces/torques acting in both cases, and then go from there. It may be helpful to draw a diagram of each case.

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(Original post by

What have you tried?

To start with, consider the forces/torques acting in both cases, and then go from there. It may be helpful to draw a diagram of each case.

**K-Man_PhysCheM**)What have you tried?

To start with, consider the forces/torques acting in both cases, and then go from there. It may be helpful to draw a diagram of each case.

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#4

(Original post by

I'm new to angular momentum and can't get my head around it, but i have tried rlly hard on this!

**student273**)I'm new to angular momentum and can't get my head around it, but i have tried rlly hard on this!

I'm sure you know Newton's Second Law for linear motion:

This law can be extended for angular motion, ie , where is the magnitude of the torque (or moment), is the moment of inertia and is angular acceleration.

Furthermore, the moment of inertia of a point particle of mass spinning around a radius is , and a compound shape made up of many parts has a moment of inertia equal to the sum of the moments of inertia of all the little parts that make it up.

Now let's consider the question:

In the first case, the two children are both exerting a force on the roundabout tangentially, ie they are applying a couple (you should have met this topic at AS-level). How do the two forces they apply add in the couple to give a resultant moment, aka a resultant torque? Then use Newton's second law for angular motion.

In the second case, one child has jumped onto the roundabout. First, you need to find the moment of inertia of this new compound object, using the hints I've given above, and consider how the other child's single force gives a resultant moment/torque, and then apply Newton's second law again. We want both angular accelerations to be constant. You should be able to work it out from here.

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(Original post by

Ok, first some theory:

I'm sure you know Newton's Second Law for linear motion:

This law can be extended for angular motion, ie , where is the magnitude of the torque (or moment), is the moment of inertia and is angular acceleration.

Furthermore, the moment of inertia of a point particle of mass spinning around a radius is , and a compound shape made up of many parts has a moment of inertia equal to the sum of the moments of inertia of all the little parts that make it up.

Now let's consider the question:

In the first case, the two children are both exerting a force on the roundabout tangentially, ie they are applying a couple (you should have met this topic at AS-level). How do the two forces they apply add in the couple to give a resultant moment, aka a resultant torque? Then use Newton's second law for angular motion.

In the second case, one child has jumped onto the roundabout. First, you need to find the moment of inertia of this new compound object, using the hints I've given above, and consider how the other child's single force gives a resultant moment/torque, and then apply Newton's second law again. We want both angular accelerations to be constant. You should be able to work it out from here.

**K-Man_PhysCheM**)Ok, first some theory:

I'm sure you know Newton's Second Law for linear motion:

This law can be extended for angular motion, ie , where is the magnitude of the torque (or moment), is the moment of inertia and is angular acceleration.

Furthermore, the moment of inertia of a point particle of mass spinning around a radius is , and a compound shape made up of many parts has a moment of inertia equal to the sum of the moments of inertia of all the little parts that make it up.

Now let's consider the question:

In the first case, the two children are both exerting a force on the roundabout tangentially, ie they are applying a couple (you should have met this topic at AS-level). How do the two forces they apply add in the couple to give a resultant moment, aka a resultant torque? Then use Newton's second law for angular motion.

In the second case, one child has jumped onto the roundabout. First, you need to find the moment of inertia of this new compound object, using the hints I've given above, and consider how the other child's single force gives a resultant moment/torque, and then apply Newton's second law again. We want both angular accelerations to be constant. You should be able to work it out from here.

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#6

(Original post by

ok so iv'e only just done first year of gcse which should explain why i'm so bad at this. so i've got the rotational inertia before as I=Mr^2 / 2 and the one after as I=(Mr^2 / 2) + mr^2. I then end up with a T of T= Fr + (Fr^2 / 2). i am so clueless at to what i am doing! sorry i'm really lost.

**student273**)ok so iv'e only just done first year of gcse which should explain why i'm so bad at this. so i've got the rotational inertia before as I=Mr^2 / 2 and the one after as I=(Mr^2 / 2) + mr^2. I then end up with a T of T= Fr + (Fr^2 / 2). i am so clueless at to what i am doing! sorry i'm really lost.

Focus on how to calculate a for each case:

Before: a = T/I = 2rF/(0.5Mr^2) = 4F/(Mr)

After: a = T*/I* = rF*/(0.5Mr^2 + mr^2)

=> a = rF*/[r^2(0.5M + m)] = F*/[r(0.5M + m)]

Now equate these expressions for a. Try form an expression for F* in terms of F, M, m, r.

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(Original post by

To add to K-Man's post, torque (T) = radius (R) x tangential force (F). You need it to sub for T in each case, so you can form the expression linking forces.

Focus on how to calculate a for each case:

Before: a = T/I = 2rF/(0.5Mr^2) = 4F/(Mr)

After: a = T*/I* = rF*/(0.5Mr^2 + mr^2)

=> a = rF*/[r^2(0.5M + m)] = F*/[r(0.5M + m)]

Now equate these expressions for a. Try form an expression for F* in terms of F, M, m, r.

**Physics Enemy**)To add to K-Man's post, torque (T) = radius (R) x tangential force (F). You need it to sub for T in each case, so you can form the expression linking forces.

Focus on how to calculate a for each case:

Before: a = T/I = 2rF/(0.5Mr^2) = 4F/(Mr)

After: a = T*/I* = rF*/(0.5Mr^2 + mr^2)

=> a = rF*/[r^2(0.5M + m)] = F*/[r(0.5M + m)]

Now equate these expressions for a. Try form an expression for F* in terms of F, M, m, r.

F(new)=2F(M+2m) / M

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#9

(Original post by

That's what I got too. What's the answer then?

**Physics Enemy**)That's what I got too. What's the answer then?

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#10

You might also want to check out the GCSE Physics Olympiad papers, available on the BPhO website (just Google it).

Either way, well done!

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#11

(Original post by

By the way, if you've only done your first year of GCSE, I wouldn't worry about this sort of question. You would only come across angular motion like this at A2 level physics/maths, in year 13. Well done for trying, and it's good that you are taking the initiative to tackle these more advanced problems, but make sure you understand everything you are learning at GCSE first, and maybe try reading about and understanding the theory first before trying the questions.

You might also want to check out the GCSE Physics Olympiad papers, available on the BPhO website (just Google it).

Either way, well done!

**K-Man_PhysCheM**)By the way, if you've only done your first year of GCSE, I wouldn't worry about this sort of question. You would only come across angular motion like this at A2 level physics/maths, in year 13. Well done for trying, and it's good that you are taking the initiative to tackle these more advanced problems, but make sure you understand everything you are learning at GCSE first, and maybe try reading about and understanding the theory first before trying the questions.

You might also want to check out the GCSE Physics Olympiad papers, available on the BPhO website (just Google it).

Either way, well done!

Typically: torque, inertia, rotational motion in general, is 1st year uni.

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**K-Man_PhysCheM**)

By the way, if you've only done your first year of GCSE, I wouldn't worry about this sort of question. You would only come across angular motion like this at A2 level physics/maths, in year 13. Well done for trying, and it's good that you are taking the initiative to tackle these more advanced problems, but make sure you understand everything you are learning at GCSE first, and maybe try reading about and understanding the theory first before trying the questions.

You might also want to check out the GCSE Physics Olympiad papers, available on the BPhO website (just Google it).

Either way, well done!

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#13

(Original post by

This isn't in a-level maths or physics either, unless you take the 'engineering' option for physics (which wasn't available till recent years). Even then, further mech is only half that option, so you don't get that many Qs on it.

Typically torque, inertia, rotational motion in general, is 1st year uni.

**Physics Enemy**)This isn't in a-level maths or physics either, unless you take the 'engineering' option for physics (which wasn't available till recent years). Even then, further mech is only half that option, so you don't get that many Qs on it.

Typically torque, inertia, rotational motion in general, is 1st year uni.

Just checked my A-level physics spec (for OCR) and yeah, you're right, no angular motion (though there is some circular motion)

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#14

(Original post by

thank you for that, i will check it out! i decided to start doing isaac physics questions because i really enjoy physics so i thought that i would practice some harder stuff. i was actually doing alright until this angular motion Q because i was really new to the concept, but otherwise i think i'm going to carry on doing wider reading around more advanced physics topics (when i say advanced i just mean a-level)!

**student273**)thank you for that, i will check it out! i decided to start doing isaac physics questions because i really enjoy physics so i thought that i would practice some harder stuff. i was actually doing alright until this angular motion Q because i was really new to the concept, but otherwise i think i'm going to carry on doing wider reading around more advanced physics topics (when i say advanced i just mean a-level)!

When you get to year 12, you'll be able to enter a competition called the "Senior Physics Challenge" on Isaac Physics. The best 40ish people get invited to a completely free residential quantum mechanics summer school at the University of Cambridge. I got to do it this year, and it was honestly one of the best experiences in my life so far and I wouldn't think twice about studying physics at Uni now.

Good luck with everything!

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#15

(Original post by

OCR is an awful syllabus, worst of the 3, unlucky you. Angular motion is in M4+ (might be M5) and considering you only need S1 & S2 for A-Level FM, it's a long shot. M3-M6 on the old pure syllabus (pre-core) was quite beastly. Infact it was typical to do (the old) M3 for A-Level Maths, and that was a hard exam in itself.

**Physics Enemy**)OCR is an awful syllabus, worst of the 3, unlucky you. Angular motion is in M4+ (might be M5) and considering you only need S1 & S2 for A-Level FM, it's a long shot. M3-M6 on the old pure syllabus (pre-core) was quite beastly. Infact it was typical to do (the old) M3 for A-Level Maths, and that was a hard exam in itself.

Yeah, I'd kinda forgotten about the stats modules tbh, I'm thinking of just doing M2,M3,M4,S2 next year (OCR again, only goes up to M4) and two pure for FM (I did C1-4 S1, M1 this year).

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#16

(Original post by

Tell me about it! Feels like we've done nothing new at all in AS-level physics, other than resolving vectors, stress/strain, some electricity things and some really qualitative "quantum mechanics", and the exam questions are annoying. Next year looks a little more interesting, though without calculus there's only so far you can go.

Yeah, I'd kinda forgotten about the stats modules tbh, I'm thinking of just doing M2,M3,M4,S2 next year (OCR again, only goes up to M4) and two pure for FM (I did C1-4 S1, M1 this year).

**K-Man_PhysCheM**)Tell me about it! Feels like we've done nothing new at all in AS-level physics, other than resolving vectors, stress/strain, some electricity things and some really qualitative "quantum mechanics", and the exam questions are annoying. Next year looks a little more interesting, though without calculus there's only so far you can go.

Yeah, I'd kinda forgotten about the stats modules tbh, I'm thinking of just doing M2,M3,M4,S2 next year (OCR again, only goes up to M4) and two pure for FM (I did C1-4 S1, M1 this year).

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#17

(Original post by

Sorry I thought you were at uni, didn't realise you just finished Y12. I didn't know you could fill up FM with so many applied units. I did FP1-FP4 and S1 & S2 on AQA for A-Level FM, back when I did it (did M1 & M2 in A-Level maths).

**Physics Enemy**)Sorry I thought you were at uni, didn't realise you just finished Y12. I didn't know you could fill up FM with so many applied units. I did FP1-FP4 and S1 & S2 on AQA for A-Level FM, back when I did it (did M1 & M2 in A-Level maths).

May I ask what you studied at Uni, and how relevant the FP units were for it? Some people have said that even for a physics degree, it would be better to do all the pure units rather than more applied, so I was just wondering what your thoughts are. Thanks

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#18

(Original post by

Yeah, OCR only goes up to FP3, and only two pure modules are compulsory.

May I ask what you studied at Uni, and how relevant the FP units were for it? Some people have said that even for a physics degree, it would be better to do all the pure units rather than more applied, so I was just wondering what your thoughts are. Thanks

**K-Man_PhysCheM**)Yeah, OCR only goes up to FP3, and only two pure modules are compulsory.

May I ask what you studied at Uni, and how relevant the FP units were for it? Some people have said that even for a physics degree, it would be better to do all the pure units rather than more applied, so I was just wondering what your thoughts are. Thanks

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#19

(Original post by

I did physics with theoretical physics (Imperial). Angular motion might be in OCR's M4. FP units were definitely useful, no need to overdo mechanics in FM because there's not much mechanics in physics or physical nat sci. Stats and Mech are equally useful, but pure/core is definitely more important than either. Also be wary about what you need to do for an A* in OCR FM and the safest route.

**Physics Enemy**)I did physics with theoretical physics (Imperial). Angular motion might be in OCR's M4. FP units were definitely useful, no need to overdo mechanics in FM because there's not much mechanics in physics or physical nat sci. Stats and Mech are equally useful, but pure/core is definitely more important than either. Also be wary about what you need to do for an A* in OCR FM and the safest route.

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**Physics Enemy**)

I did physics with theoretical physics (Imperial). Angular motion might be in OCR's M4. FP units were definitely useful, no need to overdo mechanics in FM because there's not much mechanics in physics or physical nat sci. Stats and Mech are equally useful, but pure/core is definitely more important than either. Also be wary about what you need to do for an A* in OCR FM and the safest route.

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