contestada

1. the system is made of one sphere and two rods attached to the surface of the sphere. the total moment of inertia of the system is the sum of individual moments of inertia.

Respuesta :

The total moment of inertia of the system is [tex]\frac{1}{2} ML^{2} + \frac{2}{5} MR^{2} + M(L+R)^{2}[/tex].

  • Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation.
  • Or in more simple terms, it can be described as a quantity that decides the amount of torque needed for a specific angular acceleration in a rotational axis.
  • Moment of Inertia is also known as the angular mass or rotational inertia.

Given a sphere is attached to a rod. Let the masses of both rod and sphere be M. Let, radius of sphere be R and length of rod be L.

Now,

The total moment of inertia of system is:

I (rod about end) + I (sphere about center) + Parallel axis contribution =

[tex]\frac{1}{2} ML^{2} + \frac{2}{5} MR^{2} + M(L+R)^{2}[/tex].

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