利用极坐标变换计算平面薄片的转动惯量

Calculation of the Moment of Inertia of Plane Lamina Using Polar Coordinate Transformation

运用极坐标变换和二重积分的知识,给出了平面薄片对过原点的任意轴的转动惯量的计算方法,得到了均质任意次椭圆薄片转动惯量的一个简明公式,并证明了均质任意次圆薄片对过中心的任意轴的转动惯量等于其对坐标轴的转动惯量.

The expressions for calculating the moment of inertia of a plane lamina about an arbitrary axis passing through the origin are obtained using the polar coordinate transformation and double integration methods.A simple formula for the moment of inertia of a uniform arbitrary degree elliptical plane lamina is also obtained.It is proved that the moment of inertia about an arbitrary axis passing through the center of a uniform arbitrary degree circle plane lamina is the same as that of about its x-axis.