問2.右図のようにむ軸方向の長さがa、y軸方向の長さがしで厚さを無視できる
密度が一様な長方形の薄板があり、その質量をMとする。長方形の重心O
を通り、長方形に垂直に2軸を取り、z軸周りの慣性モーメントI,を重積分
dm
を用いて求める。以下の問いに答えよ。(計 14点)
a
(1) Find the area S of the rectangle.
(2 points)
(2) Find the mass dm of the micro element using the lengths a along the r-axis and b along the y-axis as shown in the above
figure.
(2 points)
(3) Show the distance " from the center of gravity O to the micro element using z and y.
(3 points)
(4) Find the moment of inertia around zaxis I, of the rectangle using the double integral according to (4.32) formula in
P.117 of the text book. Please show a detailed calculation procedure.
(7 points)