A ball is fastened to one end of a string 0.30m long and the other end is held f

Question

A ball is fastened to one end of a string 0.30m long and the other end is held fixed at point O so that the string makes an angle of 30 degrees with the vertical. The ball rotates in a horizontal circle with the string kept at this 30 degree angle. Find the angular speed (in rad/s) of the ball in its circular path required to preserve this 30 degree angle.

Explanation / Answer

tension in the string must balance the component of weight opposite to the tension => T = mgcos30 now the horizontal component of tension must balance the centripetal force Tsin60 = mw^2R R = length of string*sin30 = .3sin30 => 3mg/4 = mw^2*.3/2 => w^2 = 5g => v = 7 rad/sec => .9g/8 = v^2

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