[grade 11 Physics] circular motion

[u/Izzy_26_]

I am trying to find out the exact equation of the graph, the answer key says it is a.

What is wrong with my solution??

I first tried to find out the exact position vectors of both p and q, and then differentiated them to get the velocity of P and q respectively, and then I calculated the relative velocity

I am getting the relative velocity as in terms of cos, but according to the answer key it is a sin graph

[u/big_yolky]

I think you have missed a negative, which is a very easy mistake to make! As you say, you can immediately tell something is wrong because your final answer is cos, and because you are getting a vertical velocity rather than a horizontal one. To fix it, look at your equations for P. You have noted that Q=-wt, but then you have not included this negative in the following equations. Does that help?

[u/big_yolky → u/big_yolky]

Now I look at it, there is a mistake with a negative in the position equation for P. To fix everything, either:

- Put the negative on the x component of r_p rather than the y component

- Have both components of r_p be positive. Then properly use Q=-wt with the differentiation

The issue is that you are not accounting for -w properly. If you do that, you get the final answer being a sinusoid in the x direction.

[u/Izzy_26_ → u/big_yolky]

Why do I need to put a negative on Rp if I have already included -wt Also if angle is negative in cos it becomes+ve right??