The ball is being spun around vertically. This means that when the ball is standing still and just hanging from the string (imagine holding a yoyo that is unwound from your finger) the tension will point upwards. In order for the ball on the string to stay in place when there is no motion at all, Force of tension = Force of gravity. If the force of gravity exceeded the Force of tension on a fixed string, then the string would break. If the Force of gravity exceeded the tension on a string that could move, then the ball would accelerate downwards. The tension on the string when the ball is at rest points upwards because it opposes the force of gravity, hence the string is tense. When the ball begins to spin in a circle, the ball will experience a centripetal acceleration inwards towards the center of the circle. This is similar to the moon in orbit around the earth. The moon does not feel a force pulling it away from the earth. Instead, the moon is actually accelerating towards the earth because it feels a force directed in towards the center of the circle. BUT, because the moon, like the ball, has tangental velocity, it avoids spiraling into the earth, like the ball avoids spiraling inwards.
The force of gravity always points towards the center of the earth, and at each point in the balls path, this direction stays the same: downward. Now as the ball starts swinging from rest, it gains velocity, and because it is moving in a circle, the velocity changes direction constantly. Assume that the ball moves from C to B to A to D and Back to C. At point C, the velocity is pointing horizontally in the direction of B( tangent to the circle at point C). At point B, the velocity is pointing vertically towards point A (tangent to the circle at point B) and so forth and so forth. SO since the velocity is constantly changing direction and is always tangent to the circle, you can see that the velocity will NEVER point in towards the center of the circle. Its velocity will always point away from the center. At B, the velocity is pointing upwards, not towards D. If an object moves in a circular motion, then it will experience a Fc inwards.
As the ball approaches point A, the ball will feel a force downwards which is equal to the sum of the Fc and the Fg. Fc = F tension. This is why Tension always points in towards the center of the circle. But the balls momentum will cause it to continue moving horizontally before falling downward, keeping the string tight. As the ball approaches point D, the tension in the string (Fc) pulls the ball inward, but Fg pulls the ball downward. The net force between the Fc and Fg follows the arc of the circle at each point in the circle because the velocity constantly changes direction.
I hope i didn't confuse you. Basically, the tension can be compared to the normal force. It is perpendicular to the line tangent to the circle at all points of the circle. Does this make sense?
This is the same reason why the F normal in picture two is pointing to the left. The normal force is always perpendicular to the surface. At the car's position, the line tangent to the circle is pointing straight up, vertically. A line perpendicular to the tangent points inwards to the left. It does not point right because the car is not moving right, and thus experiences no force to the right. Remember, circular motion, Fc. Objects feel a force that is directed in towards the center of the circle. Does this make sense?
