Consider the five following objects. Rank them in order of moment of inertia fro

Question

Consider the five following objects. Rank them in order of moment of inertia from highest to lowest. Some may be equal.

A) A point mass of mass M rotating about a fixed axis at a constant distance R from the axis.

B) A thin hoop of radius R and mass M rotating about an axis through its center and perpendicular to the plane of the hoop.

C) A thin hoop of radius 2R and mass 2M rotating about an axis through its center and perpendicular to the plane of the disk.

D) A solid disk of radius R and mass M rotating about an axis through its center and perpendicular to the plane of the disk.

E) A solid disk of radius R with a hole of radius R/2 cut from its center. The total mass of the resulting donut shaped object is M. It rotates about an axis through its center and perpendicular to its plane.

Explain why.

1 =  Highest

5 = Lowest

Explanation / Answer

2) A point mass of mass M rotating about a fixed axis at a constant distance R from the axis.

I = MR^2

2) A thin hoop of radius R and mass M rotating about an axis through its center and perpendicular to the plane of the hoop.

I = MR^2

1) A thin hoop of radius 2R and mass 2M rotating about an axis through its center and perpendicular to the plane of the disk.

I = (2M)*(2R)^2 = 8MR^2

3) A solid disk of radius R and mass M rotating about an axis through its center and perpendicular to the plane of the disk.

I = 0.5*MR^2

4) A solid disk of radius R with a hole of radius R/2 cut from its center. The total mass of the resulting donut shaped object is M. It rotates about an axis through its center and perpendicular to its plane.

I = 0.5*MR^2 - 0.5*M*(R/2)^2

= 0.375MR^2

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