Final answer:
When a system of particles is rotating about a fixed axis, the angular speed of the system can be determined using the equation ω = v/r, where ω is the angular speed, v is the linear speed of a particle in the system, and r is the distance of the particle from the axis of rotation.
Step-by-step explanation:
When a system of particles is rotating about a fixed axis, the angular speed of the system can be determined using the equation ω = v/r, where ω is the angular speed, v is the linear speed of a particle in the system, and r is the distance of the particle from the axis of rotation. In this case, since the system is rotating about the x-axis, the particles must move along the y-axis, perpendicular to the axis of rotation.
Since the rods are rigid and negligible in mass, we can assume that the particles move in circular paths around the axis of rotation. Given the angular speed of 3.80 rad/s, we can find the linear speed of the particles by multiplying the angular speed by the distance of the particle from the axis of rotation.
So, if we have a particle at a distance of y from the axis of rotation, the linear speed of the particle would be v = ωy. This equation is applicable for all three particles in the system.