AP Physics Polar Coordinates Question!

Test Preparation AP Test Preparation
1

<p>Hi,</p>

<p>So, I was doing my physics summer work and had no idea what the following question was talking about:</p>

<p>For the following polar coordinate points:</p>

<p>(4, 0) (4, 60) (4, 90) (4, 135) (4, 180) (4, 270)</p>

<p>Describe the locus of points for which</p>

<p>a) r = 4
b) r = a</p>

<p>An image, for reference, can be seen [url=<a href="http://img43.imageshack.us/img43/6422/0815002025.jpg%5Dhere%5B/b%5D%5B/url"&gt;http://img43.imageshack.us/img43/6422/0815002025.jpg]here[/url</a>].</p>

<p>Any help would be much appreciated!</p>

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<p>I do not see how this has anything to do with physics. If it is physics B, then polar is not a part of the curriculum at all. I don’t get why your teacher assigned this.</p>

<p>Well, basically you have a circle. From your reference drawing, it is centered at the pole (origin). A circle centered at the pole takes the polar form r=a where a is the radius. So r=4 is the locus (set of all points) that corresponds to the points given, and r=a is the general form of a circle centered at the pole.</p>

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<p>Thanks for your reply. :)</p>

<p>This is for physics C: m, by the way. Should have mentioned that, my bad. </p>

<p>Ah, that makes sense. Silly me, I was over analyzing it. </p>

<p>So, then (I swear this is the last one, haha) this one [**here](<a href=“http://img413.imageshack.us/img413/6007/0815002113.jpg][b]here[/url][/b”>http://img413.imageshack.us/img413/6007/0815002113.jpg)[/b</a>] would be a line of like slope something? I don’t get how one would calculate the slope though. o.O</p>

<p>Edit: the second question states: describe the locus of points for which theta = 60 and theta = theta1 (where theta1 is a fixed angle)</p>

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<p>^For that image, I don’t know what it’s asking, but you’re almost definitely going to have to convert polar coordinates to cartesian coordinates at some point. You are given polar coordinates in (r, theta) and you need to convert them to (x,y). x=r<em>cos(theta) and y=r</em>sin(theta). Once you get the cartesian coordinates of each point you can then find slopes and other stuff easily.</p>

<p>BTW there are shortcuts (like knowing the tangent) but this is the way you should learn as it won’t fail you.</p>

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<p>^^Yeah, my bad for not putting the question. I edited it in. Thanks for helping out by the way. :)</p>

<p>I had a hunch I’d have to convert the polar coordinates to Cartesian coordinates. I just did that and then so I would just use the slope formula (change in y, over change in x) with the two end points? </p>

<p>I suppose I would then put the locus for all points of which theta = 60 is a line with slope …? </p>

<p>I am still rather confused how I would answer the part of the question that says for which theta = theta1. Any ideas?</p>

<p>Thanks again! :)</p>

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<p>For this post <=theta</p>

<p>the equation <=<_1 is a general equation for a line written in polar. The angle between the line and the polar axis (x-axis) is the angle given.</p>

<p>Using SOHCAHTOA trig, you can see that tan(<)=y/x, which is the slope of the line. so the slope of <=60 is tan(60)= sqrt(3).</p>

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<p>Oh my gosh, that makes it so much easier! Thank you! :)</p>

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<p>Neither the AP Physics B or C curriculum uses polar coordinates in any significant way. But you should be very comfortable with your trigonometry and converting to and from (x,y) <-> (hypotenuse, angle). To visualize for any point, draw a right triangle with the hypotenuse going from the origin to the point and with one leg perpendicular to the x-axis.</p>