Why do hurricane winds rotate? I know it´s about Coriolis force but how can I be quantitative? My problem is that I can´t imagine the direction velocity of wind and the angle with earth angular velocity rotation. Also, when can we explain other things like bathtubs, toilets.. using Coriolis? I mean when this force is relevant to explain the motion and the direction of rotation, CCW or CW(clock wise)?
Sure coriolis force applies, but I think a much simpler intuitive explanation is conservation of angular momentum.
Think of the spinning skater who pulls in his/her arms & legs, spinning faster.
If you look down on the earth from the north star, you see a whole hemisphere covered with air rotating counterclockwise. At the pole, it's basically not moving, and at the equator it's travelling to the East at about 1000 miles per hour, so that air has huge angular momentum in the counterclockwise direction. Anything that pulls some of it together toward a point is going to increase its angular speed relative to the air around it, and vice versa.
In a hurricane you have a strong updraft of warm air, which pulls surface air toward its center, causing it to rotate counterclockwise. It gets into the inner vortex and rises, coming out at the top. As it goes outward at the top, it slows down, so appears to rotate in the opposite direction with respect to the overall air mass. So you see clouds going counterclockwise at the bottom, and clockwise at the top.
Southern hemisphere, it's just the opposite.
In a bathtub, the rotation of the earth is much less likely to be effective, compared to the way the water just happens to have been stirred.
P.S. Angular momentum is mvr, where m is mass, v is tangential velocity (meters/second), and r is radius from the center. Since it is conserved, if you reduce the radius by a factor of 10, you increase the tangential velocity by a factor of 10 (and the angular velocity (radians/second) by a factor of 100).