I have a problem that gives me the mass of saltshaker (.64 grams), radius of table (.2 meters) and the speed that the shaker is going on a spinning round table (.628m/s)
I am supposed to find the magnitude of the horizontal part of contact force on the shaker and I simply have NO idea how to start this problem

Assuming that the shaker is not sliding off the turn table as it rotates:

The centripetal acceleration of the skaker as it revolves around the center of the turntable is a=v^2/r. So from F = ma the contact force that is needed to counter-act that force is F = mv^2/r.