Bank Shots
Bank shots are all about angles and geometry.  The big question is: when you hit a ball against the rail, where will it go?  This question can be easily answered if you know how to use angles.  The general rule is the "Angle in equals Angle out".  Of course, like any other rule we know of, there are exceptions.  Certain forces such as speed an english (spin) can change the angle of the ball.
SPEED
Speed affects the angle of the ball a lot less than english does.  The more speed you put on the ball, the smaller the angle will be.  Conversely, the less speed you put on the ball, the bigger the angle will be.  In this illustration, the white line shows the ball being hit too hard (smaller angle) and the light blue line shows the ball being hit too hard (bigger angle).  The black line shows the ball being hit with the right amount of speed and making it into the pocket.
INSIDE ENGLISH
English is a very hard concept to learn, and an even harder one to master.  You apply english to the ball by not hitting it in the center, but on of the of sides.  To use inside english, you hit the cue ball on the side thats inside of the angle.  When it hits the target ball, the spin will be reversed, so it turns into outside english.  Outside english decreases the angle of the ball.  In this picture, the white line indicates the ball's path if no english was applied, and the black line indicates the balls path with the english applied to it.
OUTSIDE ENGLISH
Outside english has an exact opposite affect on the ball than inside english.  To use outside english, you need to hit the cue ball on the side that's outside the angle.  When the cue ball strikes the target ball, the spin is reversed, causing the target ball to have inside english.  Inside english, opposite from outside english, causes the angle of the ball to increase.  In this illustration, the white line indicates the ball's path had no english been performed on it, and the black line indicates the ball's path with english being applied to it.
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