A 240 g block on a 60 cm long string swings in circle on a horizontal, frictionless table at 95 rpm. What is the speed of the block? What is the tension of the string?

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> Let,

m = 240 g = 0.24 kg

L = 60 cm  = 0.6 m

> Express the given angular velocity in  radian/second ( rad/s).

`omega = 95 (rev)/min * (2pi rad)/(1 rev) *( 1 min)/(60 s)= 19/6 pi (rad)/s`

> Determine the weight of the block.

`W = mg = (0.24 kg)( (9.81 m/s) = 2.35 N`

> To solve for the tension (T) in the spring, consider the horizontal components of the forces acting on the block.

`sumF_x = 0`

`CF - Tcos theta = 0`   

where, CF is the centrifugal force

          `CF = (W/g )v^2/R = m v^2/R= m (omega R)^2/R = m omega^2R`               

          ` cos theta = R/L`    

(Note that R is the raduis of the circle formed by the rotating string.)                                    ...

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