Final answer:
The distance from the center at which a bug starts to slip on a rotating turntable can be calculated by equating the centripetal force to the maximum static friction force. Upon slipping, the bug will slide off due to inertia as the frictional force can no longer provide the necessary centripetal force to keep the bug moving in a circle.
Step-by-step explanation:
To find out how far from the center the bug gets before it starts to slip on the rotating turntable, we can use the concept of centripetal force and the coefficient of static friction. The centripetal force required to keep the bug moving in a circle is provided by the frictional force which is the product of the normal force (in this case, the bug's weight) and the coefficient of static friction. The bug will slip when the required centripetal force exceeds the maximum static friction force.
Centripetal force (Fᶜ) = m × r × ω²
Maximum static friction (Fₛ) = μₛ × m × g
Here, m is the mass of the bug, r is the radius from the center, ω is the angular velocity, μₛ is the coefficient of static friction, and g is the acceleration due to gravity. Setting these two forces equal to each other and solving for r gives us the distance from the center at which the bug will begin to slip.
After the bug moves farther out past that point, it will no longer be able to maintain its grip on the turntable due to insufficient frictional force and will slide off due to inertia.