Classical Mechanics

Moment of Inertia

Center of a mass distribution

         

A bar with length 60 cm60\text{ cm} has linear density λ=6x+12,\lambda=6x+12, where xx is in meters and λ\lambda is in kg/m.\text{kg/m}. What is the center of mass of this bar?

A rod of length 5 m5\text{ m} has density λ(x)=3+x2 kg/m,\lambda(x)=3+x^2\text{ kg/m}, and is positioned along the xx-axis with left endpoint at x=0.x=0. What is the center of mass of the rod?

Find the center of mass of a semicircular plate of radius 44 with uniform density.

Find the center of mass of the region bounded by the line y=4xy=4x and the parabola y=4x2.y=4x^2.

What is the center of mass of the region bounded by the curves y=cos7x,y=0,x=0,x=π/14,\begin{array}{c}&y=\cos 7x, &y=0, &x=0, &x=\pi/14\end{array}, given that the mass has uniform density?

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