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 centeripetal acceleration, (iv) the centeripetal force and (v) the tension in the string.

Explanation

(i) The angular velocity,
`omega = (2pi N)/(t)=(2pi xx 6)/(60)=(pi)/(5)=0.6284 rad s^(-1)`
(ii) The linear velocity, `v = r omega`
`= 0.20xx0.6284`
`= 0.1257 ms^(-1)`
(iii) The centripetal acceleration, `a_(c )=r omega^(2)`
`= 0.20xx(0.6284)^(2)`
`= 0.0790 ms^(-2)`.
(iv) The centripetal force, `F_(c )=mr omega^(2)`
`= 0.200xx0.20xx(0.6284)^(2)`
`= 0.0158 N`.
(v) The tension in the string
`= 0.0158 N`.