Question

50 POINTS !!!

Three particles of mass 8 kg, 3 kg, and 7 kg are connected by rigid rods of
negligible mass lying along the y axis and are placed at 5 m, -2 m, and -6 m,
respectively as in the figure. The system rotates about the x axis with an angular
speed of 1.65 rad/s.

a) Find the moment of inertia about the x axis. Consider the
masses to be point particles.

b) Find the total rotational energy.

c) Find the linear speed of the top particle of mass 8 kg in the figure.

Answer 1

a) I = 464 kg m², b) K = 631 .6 J, c) v = 8.25 m / s

Step-by-step explanation:

a) the moment of inertia of point particles is

I = ∑ m_i r_i²

in this case

I = 8 5² + 3 (-2) ² + 7 (-6) ²

I = 464 kg m²

b) The kinetic energy is

K = ½ I w²

K = ½ 464 1.65²

K = 631 .6 J

c) linear and angular velocity are related

v = w r

v = 1.65 5

v = 8.25 m / s