A ball of 200 g is at one end of a string of length 20 cm. It is revolved in a horizontal circle at an angular frequency of 6 rpm. Find (i) the angular velocity, (ii) the linear velocity, (iii) the centripetal acceleration, (iv) the centripetal force and (v) the tension in the string.

Explanation

(i) The angualr velocity
`omega = (2pi N)/(t) = (2pi xx 6)/60 = pi/3 = 0.6284 rad s^(-1)`
(ii) The linear velocity, `v=romega`
`=0.20 xx 0.6248 = 0.1257 ms^(-1)`
(iii) The centripetal acceleration, `a_(c) = romega^(2)`
`=0.20 xx (0.6284)^(2) = 0.0790 ms^(-2)`
(iv) The centripetal force, `F_( c) = mr omega^(2)`
`=0.200 xx 0.20 xx (0.6284)^(2) = 0.0158 N`
(v) The tension in the string `=0.0158` N