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  • Prove the theorem of parallel axes.

Q 7.26 (b)     Prove the theorem of parallel axes.
          (Hint: If the centre of mass of a system of n particles is chosen to be the origin \sum m_{i}r_{i}=0 ).

Answers (1)

best_answer

Consider the figure given below :

                                                 Rotational motion, 20191

The moment of inertia about the RS axis:- 

                                    I_{RS}\ =\ \sum m_ir_i^2

Now the moment of inertia about the QP axis:- 

                               I_{QP}\ =\ \sum m_i(a+r_i)^2

or                                        =\ \sum m_i(a^2 +r_i^2 + 2ar_i)

or                                        =\ I_{RS} + \sum m_i a^2 + 2 \sum m_iar_i^2

Thus                         I_{QP} =\ I_{RS} + M a^2                                                           \left ( \because 2\sum m_iar_i^2 \right )\ =\ 0

Hence proved.

Posted by

Devendra Khairwa

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