A child sits on a rotating merry-go-round, 2.3 m from its center. If the speed of the child is

step 1 This is a merry -go -round and this is a child. The distance from the center of this child is 2

A child sits on a rotating merry-go-round, 2.3 m from its...

A child sits on a rotating merry-go-round, $2.3 \mathrm{~m}$ from its center. If the speed of the child is $2.2 \mathrm{~m} / \mathrm{s}$, what is the minimum coefficient of static friction between the child and the merry-go-round that will prevent the child from slipping?

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Key Concepts

Static Friction

This is the frictional force that prevents an object from sliding when it is at rest relative to a surface. In situations involving circular motion, static friction can act as the centripetal force that keeps an object moving along a circular path, preventing it from slipping outward.

Coefficient of Static Friction

A dimensionless parameter that quantifies the maximum static frictional force relative to the normal force. It is defined as the ratio ? = F_friction/N and indicates how much frictional resistance exists between two surfaces in contact.

Centripetal Force

This is the force that keeps an object moving in a circular path. It is directed towards the center of the circle and is calculated using the formula F = m*v^2/r, where m is the mass of the object, v is its tangential speed, and r is the radius of the circular path.

Centripetal Acceleration

The acceleration required to maintain circular motion, which is similarly directed towards the center of the circle. It is given by the formula a = v^2/r. This concept is fundamental in understanding how forces cause objects to follow curved trajectories.

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