A stone of mass 0.50 kg is attached to an inextensible string and  whirled in a vertical circle of radius 0.98 m at a constant speed of 7.0 m/s.  Gravity g = 10 m/s²

(a) calculate the angular speed of the stone.                                                                           

(b) calculate the centripetal acceleration of the stone;                                                        

(c) the least tension in the string. (Hint: think which way gravity acts)                                

(a) v = wr  Þ w = 7.0 m/s ¸ 0.98 m  (P)

= 7.14 rad/s (P)

(b) a = v²/r = 49 m2/s2 ¸ 0.98 m (P) = 50 m/s² (P)

(c) F = ma Þ F = 0.5 ´ 50 m/s² = 25 N

Least tension is when acceleration = 50 – 10 (P)= 40 m/s²

Þ F = 20 N (P)