In which direction does static friction point?

[Warlic]

As I see it; static friction is what provides the centripetal force, but does it do anything else? When the brother applies tangential force, what will happen with the static friction, because I assume it will start to provide less centripetal force because the tangential speed of the child decreases - but will it then provide static friction against the brothers tangential force?

 

[TSny]

Is the static force of friction equal to the net force acting on the child? If so, that force must produce the total acceleration of the child.

Think about how you can break the total acceleration into components in a useful way.

 

[Warlic]

Is the static force of friction equal to the net force acting on the child? If so, that force must produce the total acceleration of the child.

Think about how you can break the total acceleration into components in a useful way.

Does the static friction have an x-component that is the centripetal force and force in the y-direction that is the tangential force - which keeps the child moving tangentially to the circle with 0.5m in radius?

 

[haruspex]

Does the static friction have an x-component that is the centripetal force and force in the y-direction that is the tangential force - which keeps the child moving tangentially to the circle with 0.5m in radius?

Whether you call them x and y like that is up to you, but yes, the static friction must account for the net acceleration, and this will have both a radial (centripetal) and tangential component.