A ball of mass m is suspended on a light string of length l from the ceiling. The ball is then put into motion such that it rotates in a horizontal circle with a rotation rate of w ( rad/s). Notice that the string makes an angle of with respect to the vertical during this motion.  A ) if the ball moved at twice it's first rotation rate, find the new angle the string would make with respect to the vertical.  B) find the tension in the string at this new rotation rate.  C) how much faster is the ball speed with this new rotation rate as compared to the oroginal speed? Find a ration of the two speed.

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Newton's First Law of Motion

If a very smooth ball is rolled down an inclined surface with zero friction, the ball will continue to roll indefinitely for an infinite time, in an attempt to reach to the same height on the opposite hill!