Rotating Frames of Reference question.

[John H]

Homework Statement

You are standing on a slowly rotating merry-go-round, turning counterclockwise as viewed from above. You are holding a string from which is suspended a rubber stopper of mass 45g. You are 2.9m from the center of the merry-go-round. You take 4.1s to complete one revolution.

A)Draw FBD of yourself in reference frame of the merry-go-round and earth(assuming to have no rotation).

B)Draw FBD of stopper in Earth's reference frame of a person looking eastward behind you.

C) Draw FBD of the stopper in your reference frame.

D) What angle does the string make with the vertical?

E) What is the magnitude of tension in the string.

Homework Equations

a_c= v^2/r

F_c=(mv^2)/r

Centripetal acceleration is also

a_c= ((4π^2 r)/T^2)

Centripetal force is also

F_c= (M)((4π^2 r)/T^2)

F= ma (Newton's second law)

The Attempt at a Solution

Here is what I attempted so far. Image is pretty big Please go to this url.

http://img801.imageshack.us/f/scan0008r.jpg/"

Thank you in advance.

 

[Mindscrape]

You don't need to use centrifugal force, and certainly not coriolis force, which only applies to something with velocity. Just use the equations for centripetal acceleration to find out how much horizontal force there and compare it with gravity's vertical force to get your angle and tension.

 

[John H]

I got the correct answer using what you told me, but I fail to understand the logic. Help would be appreciated.

 

[Mindscrape]

All the points on the outer edge of the circle have a centripetal force that is pointing towards the center of the circle. So the string you are holding has some force pushing it towards the center (you don't go towards the center because friction keeps you on the circle), and gravity has a force pulling the string down (you don't go down because the circle pushes back up on you).