# Centripetal force question (tricky)

• Apr 23rd 2008, 04:31 AM
mucky
Centripetal force question (tricky)
1. The problem statement, all variables and given/known data
1 A fairground roundabout has a number of carriages hung from a rotating circular roof by means of chains 3.5m long. The upper ends of the chains are attached to the edge of the circular roof which has a diameter of 6m. During operation, the carriages must not exceed an angle of 20º to the vertical. Draw a good annotated sketch of the roundabout and determine the maximum speed in rev.min-1 at which it can operate.

any help with formula would be amazing thanks
• Apr 23rd 2008, 10:48 AM
topsquark
Quote:

Originally Posted by mucky
1. The problem statement, all variables and given/known data
1 A fairground roundabout has a number of carriages hung from a rotating circular roof by means of chains 3.5m long. The upper ends of the chains are attached to the edge of the circular roof which has a diameter of 6m. During operation, the carriages must not exceed an angle of 20º to the vertical. Draw a good annotated sketch of the roundabout and determine the maximum speed in rev.min-1 at which it can operate.

any help with formula would be amazing thanks

Well, the radius of the motion for max angular speed will be
$r = 6 + 3.5~sin(20^o)$

$a_C = r \omega ^2$

-Dan