Three objects lie in the x, y plane. Each rotates about the z-axis with an angular speed of 6.00 rad/s. The mass m of each object and its perpendicular distance r from the z-axis are as follows:
(1) m1 = 6.00 kg and r1 = 2.00 m,
(2) m2 = 4.00 kg and r2 = 1.50 m,
(3) m3 = 3.00 kg and r3 = 3.00 m.
(a) Find the tangential speed of each object.
(b) Determine the total kinetic energy of this system using the expression
KE = ½ m1v12 + ½ m2v22 + ½ m3 v32.
(c) Obtain the moment of inertia of the system.
(d) Find the rotational kinetic energy of the system using the relation KER = ½Iω2 to verify that the answer is the same as the answer to (b).