What Is the Least Static Friction Coefficient for a Cat on a Merry-Go-Round?

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To determine the least static friction coefficient for a cat on a merry-go-round, one must analyze the forces acting on the cat. The ride has a radius of 5.4 meters and completes one rotation in 7.2 seconds, allowing for the calculation of centripetal acceleration. The centripetal force required to keep the cat in place must be compared to the gravitational force acting on it. By establishing the ratio of these forces, the minimum static friction coefficient can be derived. This analysis ensures the cat remains stationary without sliding off the ride.
Vaness330
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Hi can someone help me on this problem.

a cat dozes around merry go round at radius 5.4 meters. the ride turns on and brought up to turning rate of 7.2 seconds in one complete rotation. how do i find the least static friction coefficient between the cat and the merry go round that will allow the cat to stay in place, without sliding out.
 
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Compare the centripital force to gravitational force (the ratio).
 

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