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Homework Statement
Salve! In "The Mechanical Universe" introductory physics course, the ninth lecture called "Moving in Circles" shows the following vector equation,
Homework Equations
r = r cos w t i + r sin w t j
where i and j are vector indicators (with the little hat over them lol i=cartesian x, j=y)
The Attempt at a Solution
My question is that they display a circle and the r from the centre (radius) is spinning counter-clockwise and as it does so something strange happens. The show displays the above equation beside the circle and as the radius spins round the
or thecos w t
begin to spin around too, in what looks to me like a pattern trigonometry with an explanation. My suspicion is that there is a reason for this lol and i assume it has to do with the following pattern i noticed;sin w t
When the r points down south and proceeds spinning right, until it reaches up top (north) "cos w t" is readable and "sin w t" is upside down, then when it goes from north to south in the counter clockwise direction "cos w t" is upside down and "sin w t" is right side up. Now I wonder if this is to do with using "- sin w t" or is there an explanation somebody could give me, in laymans AND technical terms, just to quantify my fritterish thoughts. It'd really be a big help if someone would be able to help.
if my description is too ridiculous to follow you can see what I'm talking about at this link;
http://video.google.com/videoplay?docid=268446297904859913
at the 12.00 minute mark.
amabo te :)
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