Astrophysics
  • Astrophysics
@miracrown
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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Astrophysics
  • Astrophysics
thinking
Miracrown
  • Miracrown
tyt
Astrophysics
  • Astrophysics
How about a particle moves along a line of constant \(r\) from \(\theta_1\) to \(\theta_2\). Show that this is a straight line in \(r- \theta\) space but not in \(x-y\) space.

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Miracrown
  • Miracrown
|dw:1449994959409:dw|
Miracrown
  • Miracrown
|dw:1449995152151:dw|
Miracrown
  • Miracrown
this is just a sketch. Do we have to set equations to demonstrate it?
Miracrown
  • Miracrown
@Astrophysics
Miracrown
  • Miracrown
|dw:1449995239908:dw|
Miracrown
  • Miracrown
I wrote the relationship between the cartesian coordinates and the polar ones x=r*cos(theta) y=r*sin(theta)
Miracrown
  • Miracrown
I think is not easy to understand that if we increase the angle theta, then the particle moves over the circle of radius r counterclockwise, but I find it difficult to express it using equations actually
Miracrown
  • Miracrown
as this is not a straight line we can't write this expression as y=m*x+b. We know that the radius is constant (circle) and that the variable (angle) increases, that's all
Miracrown
  • Miracrown
I think we're not supposed to do a graph like... |dw:1449995572942:dw| it means the radius is contant independently on the angle theta. I think the graph is clearer
Miracrown
  • Miracrown
|dw:1449995763449:dw|