Three particles, each of mass 1.0 kg, are fastened to each other and to a rotation axis by three massless strings, each 0.120 m long, as shown in the Figure. The combination rotates around the rotation axis with an angular velocity of 25.0 rad/s in such a way that the particles remain in a straight line. What is the rotational inertia of the system?
To find the rotational inertia of the system, we need to calculate the moment of inertia for each particle and then sum them up.
The moment of inertia for a point mass rotating about an axis is given by the formula:
I = m * r^2
where I is the moment of inertia, m is the mass of the particle, and r is the perpendicular distance from the particle to the axis of rotation.
In this case, the particles are rotating in a straight line, so the perpendicular distance for each particle will be the same, equal to the length of the string, which is 0.120 m.
Now, let's calculate the moment of inertia for each particle:
I_particle = (mass of particle) * (distance from axis of rotation)^2
= 1.0 kg * (0.120 m)^2
= 0.0144 kg.m^2
Since there are three particles connected together, we need to calculate the total rotational inertia by summing up the moment of inertia for each particle:
Total rotational inertia = 3 * I_particle
= 3 * 0.0144 kg.m^2
= 0.0432 kg.m^2
Therefore, the rotational inertia of the system is 0.0432 kg.m^2.