# Need physics help with non-uniform rod inertia and KE

**Question description**

A thin rod of length *L* = 2.85 m lies along the *x*-axis with one end at the origin. The rod has a *non-uniform density* given by λ(*x*) = γ*x*^{3}, where γ = 0.50 kg/m^{4}.

Find the total mass of the rod.*M* = _____kg

Find the location of the center of mass of the rod.*X _{CM}* = _____m

Find the moment of inertia of the rod about an axis passing through the center of mass of the rod.

*I*= _______kg-m

^{2}

If the rod is spinning about an axis through the center of mass with angular speed ω = 5.00 rad/s, what is the kinetic energy of the rod?

*K*=______ J

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