- #1
bawbag
- 13
- 1
This problem is from Boas Mathermatical Methods 3ed. Section 16, problem 1.
Show that if the line through the origin and the point z is rotated 90° about the origin, it becomes the line through the origin and the point iz.
Use this idea in the following problem: Let z = ae^iωt be the displacement of a particle from the origin at time t. Show that the particle travels in a circle of radius a at velocity v = aω and with acceleration v^2 / a directed towards the centre of the circle.
I can show the first part: adding [itex]\pi[/itex] / 2 to the argument of z gives ae[itex]^{i\theta}[/itex]e[itex]^{\pi / 2}[/itex] which is just iz.
I'm not sure how to set up the second part of the problem, though. How exactly should I use this result?
Thanks
Show that if the line through the origin and the point z is rotated 90° about the origin, it becomes the line through the origin and the point iz.
Use this idea in the following problem: Let z = ae^iωt be the displacement of a particle from the origin at time t. Show that the particle travels in a circle of radius a at velocity v = aω and with acceleration v^2 / a directed towards the centre of the circle.
The Attempt at a Solution
I can show the first part: adding [itex]\pi[/itex] / 2 to the argument of z gives ae[itex]^{i\theta}[/itex]e[itex]^{\pi / 2}[/itex] which is just iz.
I'm not sure how to set up the second part of the problem, though. How exactly should I use this result?
Thanks