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I'm trying to calculate the moment of inertia of a sphere. When I calculate moment of inertia by using dI of a small disk (dI=1/2dmy^2) I have a different answer with when I calculate it through expression I=integral(r^2dm). I have two different answers. Why integral method (the second picture) doesn't work ?

Determine the weight moment of inertia (in lb · in') of the homogeneous body (shown in the image below) about the x axis. The specific weight of the material is g = 200 lb/ft3, the length /= 12 in., and the exponent in the equation a = 2.1. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. ya = x Your Answer: Answer

Using the image on the Moment of Inertia Tab, where the following criteria are considered:Assign the values to “Apply torque” = 2 Nm, “Brake force” fr = 0.2 N. “Platform Mass” m= 0.25 kg.Use"radians" for angle units. Write down the values that appear in the graphs of torque, a moment of inertia, and angular acceleration. Then, obtain the other physical quantities by applying the equations of rotational dynamics that correspond to:Time:4.5Applied torque:2 N-mBrake torque:Net torque:Angular impulse:Moment of inertia:Angular acceleration:Initial angular velocity:Final angular velocity: