Max Speed for 0.20kg Mass on Rotating Turntable

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To determine the maximum speed of a 0.20 kg cylinder on a rotating turntable, the relationship between centrifugal force and static friction must be established. The centrifugal force acting on the cylinder is calculated using the formula mass times angular velocity squared times radius. The static friction force, which prevents slipping, is derived from the normal force multiplied by the coefficient of static friction (0.080). By equating the centrifugal force to the static friction force, the maximum angular velocity can be solved for. This analysis reveals that static friction is essential for maintaining the cylinder's circular motion without slipping.
tigerseye
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I need help with this one problem:
A small metal cylinder rests on near the edge of a circular turntable that is rotating at a constant speed. The small metal cylinder has a mass of 0.20 kg, the coefficient of static friction between the cylinder and the turntable is 0.080, and the cylinder is located 0.15 m from the center of the turntable.
What is the maximum speed that the cylinder can move along its circular path without slipping off the turntable?
 
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Centrifugal force = Force due to static friction
Centrifugal force = mass*omega^2*radius
Static Force = normal force * mju
normal force = weight
mju = 0.080
equate for omega
:)
 
Static friction must provide the centripetal acceleration of the cylinder.
 

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