Four particles, each of mass 0.10 kg, are placed at the vertices of a square with sides of length 0.46 m. The particles are connected by rods of negligible mass. This rigid body can rotate in a vertical plane about a horizontal axis A that passes through one of the particles. The body is released from rest with rod AB horizontal.
(a) What is the rotational inertia of the body about axis A?
(a) What is the rotational inertia of the body about axis A?
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if I am understanding the geometry, the axis AB lies along the x axis, and the whole square rotates about the rod AB
we find the moment of inertia from I = sum (mi ri^2)
where mi is the mass of the ith particle and ri is the distance of the ith particle from the rotational axis
the two particles on the AB axis make no contribution to the moment since for them, ri=0
the other two particles contribute an amount of 0.1kg x (0.46m)^2 = 0.0211kgm^2
since there are two particles contributing this amount, the moment of inertia about the rotational axis AB is 0.0422 kgm^2
if this is not the correct geometry, apply the definition of sum(mi ri^2)
we find the moment of inertia from I = sum (mi ri^2)
where mi is the mass of the ith particle and ri is the distance of the ith particle from the rotational axis
the two particles on the AB axis make no contribution to the moment since for them, ri=0
the other two particles contribute an amount of 0.1kg x (0.46m)^2 = 0.0211kgm^2
since there are two particles contributing this amount, the moment of inertia about the rotational axis AB is 0.0422 kgm^2
if this is not the correct geometry, apply the definition of sum(mi ri^2)