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) = γx3, where γ = 0.50 kg/m4.
Find the total mass of the rod.
M = _____kg
Find the location of the center of mass of the rod.
XCM = _____m
Find the moment of inertia of the rod about an axis passing through the center of mass of the rod.
I = _______kg-m2
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