• Support PF! Buy your school textbooks, materials and every day products Here!

Motion in Polar Coordinates problem

  • Thread starter Master J
  • Start date
  • #1
226
0
Been looking over past exam questions and came across this one. Its in polar coordinates:

A particle P describes the curve r=be^[Zcot(a)].

Show that the velocity and acceleration vectors have angles a and 2a with OP (O is the origin).

Z is actually theta, the angle the position vector makes with the x axis. Its derivative to time is w, a constant here. B and a are constants.


I'm stumped!!!!


I work out v as: bcot(a)we^(Zcot(a)).[e_1] + bwe^('').[e_2]

Even with them worked out I am stumped as to show that^^^^

Any pointers???

Cheers guys!!!
 

Answers and Replies

  • #2
alphysicist
Homework Helper
2,238
1
Hi Master J,

Been looking over past exam questions and came across this one. Its in polar coordinates:

A particle P describes the curve r=be^[Zcot(a)].

Show that the velocity and acceleration vectors have angles a and 2a with OP (O is the origin).

Z is actually theta, the angle the position vector makes with the x axis. Its derivative to time is w, a constant here. B and a are constants.


I'm stumped!!!!


I work out v as: bcot(a)we^(Zcot(a)).[e_1] + bwe^('').[e_2]
I would suggest first simplifying this expression for v, using the expression for r given in the problem. Then, since they ask for the angle between two vectors, that suggests using the dot product (since one definition of the dot product explicitly includes the angle between the vectors). Do you get the answer?
 
  • #3
226
0
SOlved! Thanks for the help.
 
  • #4
alphysicist
Homework Helper
2,238
1
Sure, glad to help!
 

Related Threads for: Motion in Polar Coordinates problem

Replies
3
Views
7K
Replies
1
Views
3K
Replies
9
Views
3K
Replies
5
Views
3K
  • Last Post
Replies
12
Views
1K
  • Last Post
Replies
4
Views
153
  • Last Post
Replies
11
Views
5K
  • Last Post
Replies
1
Views
2K
Top