Multivariable Calculus · 免费预览

质心与矩

密度变化的薄片的质量与矩，质心作为加权平均，以及旋转体的转动惯量。

1. Mass and the balance point

Mass and the balance point

A worked lamina

Moments of inertia

The same machinery in space

The triangle with vertices $(0,0)$ , $(1,0)$ , $(0,1)$ carries density $x + y$ . What is its mass?

With mass $1/3$ and moments $M_x = M_y = 1/8$ , where is the center of mass?

Two wheels have equal mass, one solid and one rim-weighted. Which spins up more easily?

A uniform-density ball centered at the origin has moment $\iiint x\, \delta\, dV$ about the yz-plane. Give its value, as a plain number.

A lamina has mass $2$ and moment of inertia $I = 8$ about an axis. Give the radius of gyration, as a plain number.

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