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    I was trying to help somebody out on TSR with a basic momentum question, me being me, decided to complicate it and make it all fancy looking with polar vectors and shizzle... long story short, I realised I don't know how to add vectors in polar form.

    I haven't learned this yet and have no idea what technique it uses, heck I haven't been taught polar form yet [by my teacher], so I was hoping someone could help me?

    \vec{v}_a = \langle v_a,\theta_a^{\circ}\rangle\quad  \vec{v}_b = \langle v_b,\theta_b^{\circ}\rangle\\ \\ \vec{P}_a = m_a\cdot\langle v_a,\theta_a^{\circ}\rangle\quad  \vec{P}_b = m_b\cdot\langle v_b,\theta_b^{\circ}\rangle\\ \\ \vec{P}_a +\vec{P}_b = \text{wadafook?}

    I appreciate any help...and holy crap latex takes forever to type.
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    (Original post by Callum Scott)
    I appreciate any help...and holy crap latex takes forever to type.
    I'd convert them to cartesian, perform the addition componentwise, and then convert back.

    Edit: PS. I wouldn't use polar form for basic momentum questions.
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    (Original post by ghostwalker)
    I'd convert them to cartesian, perform the addition componentwise, and then convert back.

    Edit: PS. I wouldn't use polar form for basic momentum questions - I assume this is A-level.
    I got
    \vec{P}_T = [m_a v_a\cos{(\theta_a^{\circ})}+m_b v_b\cos{(\theta_b^{\circ})}]\mathbf{i} + [m_a v_a\sin{(\theta_a^{\circ})}+m_b v_b\sin{(\theta_b^{\circ})}]\mathbf{j}

    But I looked at that and thought...there must be an easier way :coma:
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    (Original post by Callum Scott)
    I got
    \vec{P}_T = [m_a v_a\cos{(\theta_a^{\circ})}+m_b v_b\cos{(\theta_b^{\circ})}]\mathbf{i} + [m_a v_a\sin{(\theta_a^{\circ})}+m_b v_b\sin{(\theta_b^{\circ})}]\mathbf{j}

    But I looked at that and thought...there must be an easier way :coma:
    Yep, looks good.

    And nope, no easier method.

    Your question is akin to asking what is the sum of two complex numbers given in polar form. Polar form is useful if you want to multiply or divide them, but rather a pig for adding and subtracting.
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    (Original post by ghostwalker)
    Edit: PS. I wouldn't use polar form for basic momentum questions.
    This brings up a good question, when DO you use polar form? For complex numbers it's easy to see the benefits, but I'm struggling to find a use for them when it comes to vectors.
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    (Original post by Callum Scott)
    I appreciate any help...and holy crap latex takes forever to type.
    But it looks beautiful, doesn't it? I mean compared to your average maths TSR question, which are ugh... so damn ugly lol!
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    (Original post by gagafacea1)
    But it looks beautiful, doesn't it? I mean compared to your average maths TSR question, which are ugh... so damn ugly lol!
    Very true! lol, it's definitely worth the agony; i only heard about it today and was like, "I must learn this language".
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    (Original post by Callum Scott)
    Very true! lol, it's definitely worth the agony; i only heard about it today and was like, "I must learn this language".
    You'll definitely get faster in time. Btw LaTeX IS used by a lot of academics when writing papers, whether it be for maths or biology. If you have seen a few papers online then you might have noticed that they all have a certain similar template. Oh and it's also used by Cambridge for the Maths exams.
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    (Original post by gagafacea1)
    You'll definitely get faster in time. Btw LaTeX IS used by a lot of academics when writing papers, whether it be for maths or biology. If you have seen a few papers online then you might have noticed that they all have a certain similar template. Oh and it's also used by Cambridge for the Maths exams.
    that's good to know, accidentally helping my-future-self out here lol
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    (Original post by Callum Scott)
    that's good to know, accidentally helping my-future-self out here lol
    tbh I had the same reaction when I found out. What A levels are you doing btw? Because I've never done polar form in vectors.
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    (Original post by gagafacea1)
    tbh I had the same reaction when I found out. What A levels are you doing btw? Because I've never done polar form in vectors.
    Just did Maths, F maths, Physics and Chemistry for AS, but now I've dropped chemistry for A2 [all edexcel now].
    I was reading a bit about what we learn in physics A2 and there was a formula, a_c = \frac{v^2}{r} [giggity]; I wanted to learn to prove it and so watched a calculus proof from Khan Academy and it was there, whereupon I was bestowed with the gift that was the knowledge of the existence of polar vectors
    Then when that guy asked the momentum question with angles and magnitudes, I thought...omg, polar vectors are so cool, let's use them... to my disappointment

    Edit: wait no, I just lied to myself, he used normal vectors, I have no idea where I learned the polar form from :borat: -- seemed pretty intuitive to me when doing the momentum question
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    (Original post by Callum Scott)
    Just did Maths, F maths, Physics and Chemistry for AS, but now I've dropped chemistry for A2 [all edexcel now].
    I was reading a bit about what we learn in physics A2 and there was a formula, a_c = \frac{v^2}{r} [giggity]; I wanted to learn to prove it and so watched a calculus proof from Khan Academy and it was there, whereupon I was bestowed with the gift that was the knowledge of the existence of polar vectors
    Then when that guy asked the momentum question with angles and magnitudes, I thought...omg, polar vectors are so cool, let's use them... to my disappointment
    I was gonna do physics, but after OCR I was like "NOPE! I am DONE with this bull****!" And decided I'm gonna do chemistry instead.
    Also is that the formula for centripetal acceleration?
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    (Original post by gagafacea1)
    I was gonna do physics, but after OCR I was like "NOPE! I am DONE with this bull****!" And decided I'm gonna do chemistry instead.
    Also is that the formula for centripetal acceleration?
    Indeed! I don't even like A level physics [as of yet], everything's so loose and wishy washy. They don't even tell us that calculus is linked to mechanics the fookin end of bells. Suvat equations can be derived from calculus...NOT EVEN A WORD IS SAID. It's more important to know that a spring has an innate 'stiffness constant'?! WHAT CAUSES IT, HOW DO YOU KNOW ITS CONSTANT?! *cough*...sorry it peeves me sometimes
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    (Original post by gagafacea1)
    This brings up a good question, when DO you use polar form? For complex numbers it's easy to see the benefits, but I'm struggling to find a use for them when it comes to vectors.
    Central forces (circular motion is a special case)
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    (Original post by Callum Scott)
    Indeed! I don't even like A level physics [as of yet], everything's so loose and wishy washy. They don't even tell us that calculus is linked to mechanics the fookin end of bells. Suvat equations can be derived from calculus...NOT EVEN A WORD IS SAID. It's more important to know that a spring has an innate 'stiffness constant'?! WHAT CAUSES IT, HOW DO YOU KNOW ITS CONSTANT?! *cough*...sorry it peeves me sometimes
    yes yes yes yes yes yes yes yes YES!! This is IT! We were doing waves last year, and by the end I was still asking myself, the HELL is a wave?? I still don't know lol. How is it formed? Nope, still don't know. Of course I can go online, which I did and I do have a little of a basic understanding. I feel like they just want to cover everything, it's like a damn kids crash course!
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    (Original post by gagafacea1)
    yes yes yes yes yes yes yes yes YES!! This is IT! We were doing waves last year, and by the end I ended up asking myself, the HELL is a wave?? I still don't know lol. How is it formed? Nope, still don't know. Of course I can go online, which I did and I do have a little of a basic understanding. I feel like they just want to cover everything, it's like a damn kids crash course!
    I remember at GCSE, they said that the number of electrons that can inhabit electron shells goes 2,8,8,8,8,8... But when you look at the noble gases (ATOMS WITH FILLED SHELLS), you could clearly see that the electron number did not go in that order! When I asked about it, she said..."oh, you don't need to know about that (WE'RE JUST GOING TO LIE TO YOUR FACE), that's something you'll cover in college, at AS level". They tell you that motor forces follow fleming's left hand rule...they don't tell you a thing about maxwell's equations and why that happens.
    I have so many instances where this is the case, and me asking questions is probably why I do better than these kids that are taught facts blindly, with no understanding, and are expected to sponge it in for the exams

    *breathes*
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    (Original post by Callum Scott)
    ...and holy crap latex takes forever to type.
    But when you're used to it, it's very quick. I'm aware of people who can type in-line maths in real time :zomg:
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    (Original post by Callum Scott)
    I remember at GCSE, they said that the number of electrons that can inhabit electron shells goes 2,8,8,8,8,8... But when you look at the noble gases (ATOMS WITH FILLED SHELLS), you could clearly see that the electron number did not go in that order! When I asked about it, she said..."oh, you don't need to know about that (WE'RE JUST GOING TO LIE TO YOUR FACE), that's something you'll cover in college, at AS level". They tell you that motor forces follow fleming's left hand rule...they don't tell you a thing about maxwell's equations and why that happens.
    I have so many instances where this is the case, and me asking questions is probably why I do better than these kids that are taught facts blindly, with no understanding, and are expected to sponge it in for the exams

    *breathes*
    And that's why I hated GCSE's even more! They need to do separate A levels for people actually wanting to study the subject and people taking it just because! A level physics is an abomination AND an insult to theoretical physics.
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    (Original post by Callum Scott)
    Indeed! I don't even like A level physics [as of yet], everything's so loose and wishy washy. They don't even tell us that calculus is linked to mechanics the fookin end of bells. Suvat equations can be derived from calculus...NOT EVEN A WORD IS SAID. It's more important to know that a spring has an innate 'stiffness constant'?! WHAT CAUSES IT, HOW DO YOU KNOW ITS CONSTANT?! *cough*...sorry it peeves me sometimes
    1) You've assumed constant acceleration - what more needs to be said!? Integrate for one equation, and integrate again for a second, and then rearrange some stuff for the others.

    2) Well, cause aside, I would've thought your teacher would've explained it's a constant because, doing the experiment, you get a linear relationship between force and extension. I guess you might question the generalisation to other materials..
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    (Original post by gagafacea1)
    And that's why I hated GCSE's even more! They need to do separate A levels for people actually wanting to study the subject and people taking it just because! A level physics is an abomination AND an insult to theoretical physics.
    I have students in my physics class that thought the maths was too hard last year, but because they find it interesting, plan on doing it in uni..and I'm there like... "*****?! Do you even know what a second order differential equations is?" *snaps fingers*

    But all joking aside, people seriously consider physics when they're crap at maths because they aren't being told that physics is basically 100% maths at uni, or being taught in that way. My physics teacher winces when he has to say the world maths because people moan about it all of the time
 
 
 
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