Chapter 13, Problem 18PQ

The system shown in Figure P13.18 consisting of four particles connected by massless, rigid rods is rotating around the x axis with an angular speed of 2.50 rad/s. The particle masses are m₁ = 1.00 kg, m₂ = 4.00 kg, m₃ = 2.00 kg, and m₄ = 3.00 kg. a. What is the rotational inertia of the system around the x axis? b. Using $K_r=\frac{1}{2}I{\omega }^2$ (Eq. 13.10), what is the total rotational kinetic energy of the system? c. What is the tangential speed of each of the four particles? d. Considering the system as four particles in motion and using $K={\displaystyle {\sum }_i\frac{1}{2}m{v}_i^2}$, what is the total kinetic energy of the system? How does this value compare with the result obtained in part (b)?

FIGURE P13.18