Each of the following objects has a radius of 0.214 m and a mass of 2.15 kg, and

Question

Each of the following objects has a radius of 0.214 m and a mass of 2.15 kg, and each rotates about an axis through its center (as in this table) with an angular speed of 38.9 rad/s. Find the magnitude of the angular momentum of each object.

(a) a hoop
(b) a solid cylinder

c) a hollow spherical shell

Moments of Inertia for Various Rigid Objects of Uniform Composition Hoop or thin Solid sphere cylindrical shell MR2 MR2 Solid cylinder Thin spherical or disk. shell MR2 MR Long, thin rod Long, thin with rotation axis rod with through center rotation axis through end ML ML

Explanation / Answer

L = Iw

Let's start with calculating moment of inertia (I)

Hoop= MR^2 = (2.15) ( 0.214)^2 = 0.098 kg m^2

L ( Hoop) = 3.83

Solid Cylinder = 1/2mr^2= 0.049

L ( solid cylinder) = 1.915

Hollow Speherical Shell = 2/3 mr^2= 2/3 ( 0.098 )

L= 2.541

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