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# Moment of Inertia

A sewer pipe rolls more slowly down an incline than a bowling ball with the same mass. Understand this and more by learning about Moment of Inertia, a measure of how compact objects are.

# Center of a mass distribution

A bar with length $$60\text{ cm}$$ has linear density $$\lambda=6x+12,$$ where $$x$$ is in meters and $$\lambda$$ is in $$\text{kg/m}.$$ What is the center of mass of this bar?

A rod of length $$5\text{ m}$$ has density $$\lambda(x)=3+x^2\text{ kg/m},$$ and is positioned along the $$x$$-axis with left endpoint at $$x=0.$$ What is the center of mass of the rod?

Find the center of mass of a semicircular plate of radius $$4$$ with uniform density.

Find the center of mass of the region bounded by the line $$y=4x$$ and the parabola $$y=4x^2.$$

What is the center of mass of the region bounded by the curves $\begin{array} &y=\cos 7x, &y=0, &x=0, &x=\pi/14\end{array},$ given that the mass has uniform density?

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