Math Problem Statement

En el péndulo de la figura, se solicita calcular su momento de inercia de masa Im, respecto a un eje perpendicular al papel, que pasa por el punto P y determinar la posición de su centro Cm.

Solution

To solve this, we need to calculate two things:

  1. Moment of Inertia about point PP:

    • The moment of inertia of the rod (Im(Barra)I_m(\text{Barra})) is already given as: Im(Barra)=13mL2I_m(\text{Barra}) = \frac{1}{3} m L^2
    • The moment of inertia of the square plate is calculated using the parallel axis theorem, combining its moment of inertia about its center (112ma2\frac{1}{12}ma^2) and the distance from CC to PP.

  2. Position of Center of Mass (CmC_m):

    • Use the center of mass formula, weighted by the mass and position of each object.

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Math Problem Analysis

Mathematical Concepts

Moment of Inertia
Center of Mass
Parallel Axis Theorem

Formulas

Moment of inertia of a rod: Im(Barra) = (1/3) m L^2
Moment of inertia of a plate: Im(Placa) = (1/12) m a^2
Parallel Axis Theorem: I = I_center + m d^2
Center of mass: x_cm = Σ(m_i x_i) / Σ(m_i)

Theorems

Parallel Axis Theorem

Suitable Grade Level

College-level Mechanics

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