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Goryan [66]
2 years ago
11

Which statement best describes this situation

Physics
1 answer:
nasty-shy [4]2 years ago
3 0

Answer:

what situation?

Explanation:

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A thin, uniform rod is bent into a square of side length a. If the total mass is M, find the moment of inertia about an axis thr
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Answer:

The  moment of inertia about an axis through the center and perpendicular to the plane of the square is

    I_s =  \frac{Ma^2}{3}

Explanation:

From the question we are told that

   The length of one side of the square is  a

   The total mass of the square is  M

Generally the mass of one size of the square is mathematically evaluated as

    m_1 = \frac{M}{4}

Generally the moment of inertia of one side of the square is mathematically represented as

        I_g =  \frac{1}{12}  *  m_1 * a^2

Generally given that m_1 = m_2 = m_3 = m_4 = m it means that this moment inertia evaluated above apply to every side of the square  

Now substituting for  m_1

  So

       I _g=  \frac{1}{12}  *  \frac{M}{4} * a^2

Now according to  parallel-axis theorem the moment of inertia of one side of the square about an axis through the center and perpendicular to the plane of the square is mathematically represented as

      I_a =  I_g + m [\frac{q}{2} ]^2

=>    I_a =  I_g + {\frac{M}{4} }* [\frac{q}{2} ]^2

substituting for I_g

=>    I_a =  \frac{1}{12}  *  \frac{M}{4} * a^2 + {\frac{M}{4} }* [\frac{q}{2} ]^2

=>    I_a = \frac{Ma^2}{48} + \frac{Ma^2}{16}

=>    I_a = \frac{Ma^2}{12}

Generally the moment of inertia of the square about an axis through the center and perpendicular to the plane of the square is mathematically represented as

      I_s = 4 * I_a

=>   I_s = 4 * \frac{Ma^2}{12}

=>   I_s =  \frac{Ma^2}{3}

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