In circular motion the acceleration points towards the centre: by the second law there must exist a net centripetal force Fc=mv2/r=mω2rF_c = mv^2/r = m\omega^2 r. It is not a new force, but the resultant of the forces already present — tension, gravity, friction, normal reaction, elastic force. From here: a car on a bend, the conical pendulum, banked curves, the rotating spring.

Try it — interactive simulation

Balls on a rotating platform seen from above: static friction supplies the centripetal force while it can, then the ball flies off along the tangent. The dashed red ring is the critical radius: beyond it friction is no longer enough. The red arrow on the big ball shows the friction force required; once it flies off it turns orange with its velocity. Adjust rotation and friction.