Question

A stone is whirled in a vertical circle as shown in the figure below using a string of length 40 cm. A, B, C and D are various positions of the stone in its motion. The stone makes 2 revolutions per second and has a mass of 100g.

1. Calculate:
   • The angular velocity 
   • The tension on the string at position A 
2. At C where the stone has acquired a constant angular speed, the string cuts. The stone takes 0.5 seconds to land on the ground. How high is point C above the ground.
3. How far does it travel horizontally before hitting the ground. 

Answer 1

1.   
   • w = 2πf
     2 x 3.142 x 2
     12.568 rads^-1 
   • T_A = mrw² = mg
     0.1 x 0.4 x 12.568² - 0.1 x 10
     T_A = 5.318N
      
2. h = ¹/₂gt²
   0.5 x 10 x 0.5²
   h= 1.25m
    
3. v=wr
   12.568 x 0.4
   5.027m/s
   R = ut
   5.027 x 0.5
   2.514m