Question

In Fig. 10-32, three 0.04 kg particles have been glued to a rod of length L = 13 cm and negligible mass and can rotate around a perpendicular axis through point O atone 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)?

Answer 1

a) Work Required = change in K.E
= 1/2 I w_f² -1/2 Iw_i² (I = moment of inertia of the system)

AlsoI = 3 x m L²

= 2.028 x 10^-3 kg m²

=> W =2.028 x 10^-3 x20²/2 = 0.4056 J

b)Work Required = 1/2 x2.028 x 10^-3 x( 40² -20²)

= 1.2168 J

c)Work Required =1/2 x2.028 x 10^-3x( 60²-40²)

= 2.028 J

d) Slope = 1/2 I

= 1.014 x 10^-3