A rigid circular platform rotates with constant angular speed ω about a vertical axis through its centre. Two insects X and Y, of masses m and 2m respectively, stand at fixed distances r and 2r from the axis.
a. (i) Obtain algebraic expressions for the centripetal accelerations aX and aY of insects X and Y in terms of ω and r.
b. (ii) Show that the ratio of the horizontal forces that must act on the insects to keep them in their circular paths is 1:4.
c. (iii) The angular speed of the platform is increased by 50\%. Determine the new ratio of the centripetal accelerations of X and Y.
d. (iv) Comment briefly on how the change in angular speed affects the magnitude of the required horizontal force on each insect.