In Figure, three 0.0100 kg particles have been glued to a rod of length L = 6.00 cm and negligible mass and can rotate around a perpendicular axis through point O at one end. How much work is required to change the rotational rate?

(a) From 0 to 20.0 rad/s,

(b) From 20.0 rad/s to 40.0 rad/s, and

(c) From 40.0 rad/s to 60.0 rad/s?

(d) What is the slope of a plot of the assembly's kinetic energy (in joules) versus the square of its rotation rate (in radians-squared per second-squared)?