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Problem:  An object is formed by attaching a uniform, thin rod with a mass of mr = 6.85 kg and length L = 5.76 m   to a uniform sphere with mass ms = 34.25 kg and radius R = 1.44 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 = 460 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 = 460 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?

FREE Expert Solution

Moment of inertia for a point mass:

I=MR2

Moment of inertia of a solid sphere:

I=25MR2

Moment of inertia of a rod about the end:

I=13ML2

Newton's second law for the angular motion:

τ=Iα, where τ is the net external torque, I is the moment of inertia, and α is the angular acceleration.

Torque:

τ=r×F

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Problem Details

 An object is formed by attaching a uniform, thin rod with a mass of mr = 6.85 kg and length L = 5.76 m   to a uniform sphere with mass ms = 34.25 kg and radius R = 1.44 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 = 460 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 = 460 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?

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