An object is formed by attaching a uniform, thin rod with a mass of m r = 6.98 k

Question

An object is formed by attaching a uniform, thin rod with a mass of mr = 6.98 kg and length L = 5.04 m to a uniform sphere with mass ms = 34.9 kg and radius R = 1.26 m. Note ms = 5mr and L = 4R.

1)

What is the moment of inertia of the object about an axis at the left end of the rod?  

kg-m2

2)

If the object is fixed at the left end of the rod, what is the angular acceleration if a force F = 401 N is exerted perpendicular to the rod at the center of the rod?

rad/s2

3)

What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)  

kg-m2

4)

If the object is fixed at the center of mass, what is the angular acceleration if a force F = 401 N is exerted parallel to the rod at the end of rod?

rad/s2

5)

What is the moment of inertia of the object about an axis at the right edge of the sphere?

kg-m2

6)

Compare the three moments of inertia calculated above:  

ICM < Ileft < Iright

ICM < Iright < Ileft

Iright < ICM < Ileft

ICM < Ileft = Iright

Iright = ICM < Ileft

momentofinertia3 What is the moment of inertia of the object about an axis at the right edge of the sphere? kg-m2 6) Compare the three moments of inertia calculated above: ICM

Explanation / Answer

What is the moment of inertia of the object about an axis at the left end of the rod?

1/3 Mr L^2 + (2/5 Ms R^2 + Ms (L + R)^2

= 1/3*6.99*5.04*5.04 + (2/5*34.95*1.26*1.26 + 34.95*(5.04+1.26)*(5.04+1.26))

= 1468.545876

= 1470 kg.m2

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