An object is formed by attaching a uniform, thin rod with a mass of mr = 6.57 kg

Question

An object is formed by attaching a uniform, thin rod with a mass of mr = 6.57 kg and length L = 5.2 m to a uniform sphere with mass ms = 32.85 kg and radius R = 1.3 m. Note ms = 5mr and L = 4R. https://www.smartphysics.com/Content/Media/Images/Mechanics/15/momentofinertia1new.png above is an image that demonstrates the first few problems before the axis of rotation is changed. 1) What is the moment of inertia of the object about an axis at the left end of the rod? 2) If the object is fixed at the left end of the rod, what is the angular acceleration if a force F = 476.0 N is exerted perpendicular to the rod at the center of the rod? 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.) 4) If the object is fixed at the center of mass, what is the angular acceleration if a force F = 476.0 N is exerted parallel to the rod at the end of rod? 5) What is the moment of inertia of the object about an axis at the right edge of the sphere?

Explanation / Answer

I'm not quite sure of your configuration here but here's how you solve it. (a) Find the location of the center of mass of the system. That's easy; you know the mass of the sphere and the location of it's center of mass, and you know the mass of the rod and the location of it's center of mass. (b) Compute the moment of inertia of the sphere about the center and of the rod about it's center. (c) Use the parallel axis theorem to find the moment of inertia of each object about the location of the center of mass. (d) Add 'em up. That's the moment of inertia of your system.

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