Moment of Inertia

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Derive the *Parallel Axis Theorem*.

Derive the *Perpendicular Axis Theorem*.

Calculate the moment of inertia of a body of mass *M* relative to an axis at a distance *D*,

A system consists of two bodies of mass *M* and *m* (*M*>*m*) connected by a rod
of negligible mass, the distance between its centers is equal to *R*. Calculate the moment of
inertia relative to an axis passing through the center of mass of the system.

A system with four point bodies connected by bars of negligible mass, located at the corners of a square
of side *R*. Calculate the moment of inertia about an axis passing through the center of the square
and perpendicular to the plane containing the masses at the following cases:

a) The four bodies have masses equal to*M*;

b) The bodies have masses equal to 1 kg, 2 kg, 3 kg, 4 kg, and*R* = 2 m.

a) The four bodies have masses equal to

b) The bodies have masses equal to 1 kg, 2 kg, 3 kg, 4 kg, and

A system has three masses connected by bars with negligible masses which are located at the points
indicated in the figure.

a) Calculate the position of the*Center of Mass* of this system;

b) Calculate the*Moment of Inertia* about the *Center of Mass* of the system.

The masses and positions of the bodies are:*m*_{A} = 5 kg,
(*x*_{A}, *y*_{A}) = (8, 0), *m*_{B} = 7 kg,
(*x*_{B}, *y*_{B}) = (–4, 6) and *m*_{C} = 2 kg,
(*x*_{C}, *y*_{C}) = (1, –2).

a) Calculate the position of the

b) Calculate the

The masses and positions of the bodies are:

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