Total Kinetic Energy difference to rotational kinetic energy
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A thin stick of length L = 1.6 m is denser at one end than at the other: Its mass density is = (0.40 kg/m) - (0.03 kg/m^2)x, where x measures the distance from the heavier end of the stick. The stick rotates with period T = 1 s about an axis perpendicular to the stick through the heavy end. Determine the rotational kinetic energy, KR of the stick.
Would the total kinetic energy be different than the rotational kinetic energy?
10.13 J
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The moment of inertia of a point mass is given by I = mR^2 , but the stick would have to be considered as an infinite number of point masses, and each must be multiplied by the square of its distance from the axis.
So the moment of inertia is given by, I = integral (from 0 to L) of (r^2 dm)
The mass element dm can be expressed in terms of a length element dR ...
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