Position Vectors: Get Help & Understand Concepts

[Erkan Tur]

Homework Statement

Homework Equations

Relevant equations can be derived from the formulas, by exchanging x to v, v to a, etc.

The Attempt at a Solution

I've tried to graph them, but I am not able to visualize or understand them.

Please help me about these questions, I need some hints.

If you can suggest me some parts or questions relevant to this topic, I will be so happy because I cannot understand this concept.

 

[Joydeep Munshi]

Hi,

the info given in qn is not correct. here angle theta cannot be between r and z axis. as in that case theta becomes 90 degree and that doesn't make sense. theta is between r vector and x-axis and in that case it is just a transformation between rectangular and polar coordinates in 2-D. Please check attachment for your help. I guess you can try qn. c and qn. d now
.

 

[Erkan Tur]

Hello,
I was looking for it also, thank you for your kind reply and your work, I am trying to visualize the angle for the z axis, since there is no component for the z hat plane, it doesn't make sense thus it is 90 degrees. I agree with you, neverthless I told them this morning, but he told that there is more to think about that point. Thank you for your help, I understood your kind help correctly. Do you have any books in your mind, about the part of this classical mechanics?

 

[Erkan Tur]

But if we neglect that z part and exchange with x hat, it is reasonable. Thank you anyway kind friend, I will be solving it as x

 

[Joydeep Munshi]

Hi,

See if the angle is between Z axis and r vector than definitely r hat becomes y hat and theta hat becomes (-ve) x hat. from that perspective it is a rotation of the vector by 90 deg if you transform from rectangular to the r-theta co-ordinate.

You can follow Spiegel for concepts on Vectors and Curvilinear co ordinates.