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**1. Homework Statement**

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.

**2. Homework Equations**

I don't know whether to enter the circular roof's radius of 3 m in the equation below, ie add it to the 3.5 m long chain?

**3. The Attempt at a Solution**

Without addition of the roofs radius of 3 m:

[tex]\sqrt{}(9.81tan20)/(3.5sin20)[/tex] = 1.727rad.sec

1.727 x 60 / 2[tex]\pi[/tex] = 16.49 rpm

Addition of the radius of 3 m:

[tex]\sqrt{}(9.81tan20)/(6.5sin20)[/tex] = 1.267rad.sec

1.727 x 60 / 2[tex]\pi[/tex] = 12.10 rpm

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