Question

An object is formed by attaching a uniform, thin rod with a mass of m-7.28 kg and length L-5.64 m to a unlform sphere with mass ms-36.4 kg and radius R-1.41 m. ?te ms-5m, and L-4R. ) What is the moment of inertia of the object about an axis at the left end of the rod? g-m2 Submit You currently have O submissions for this question. Only 9 submisslon are allowed. You can make 9 more submissions for this question. 2) If the object is fixed at the left end of the rod, what is the angular acceleration if a force F 491 N is exerted perpendicular to the rod at the center of the rod? ad/s Submit You currently have 0 submissions for this question. Only 9 submission are atlowed. You can make 9 more submissions for this question 3) What is the moment of inertia of the object about an axds 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-) You currently have 0 submissions for this question. Only 9 submission are allowed. You can make 9 more submissions for this question 4) If the object is fixed at the center of mass, what is the angular acceleration if a force F 491 N is xerted parallel to the rod at the end of rod? Submit You currently have O submissians for this question. Only 9 submission are allowed You can make 9 more submissions for this question. S) What is the moment of inertia of the object about an axis at the right edge of the sphere? m2 Submit You currently have o submissions for this question. Only 9 submission are allowed. You can make 9 more submisslons for this question. 6) Compare the three moments of inertia calculated above: lcwlu-righ Submit

Answer 1

This problems is based on the calculate of moment of inertia (MoI) and the application of parallel axis theorem. Theorem of parallel Axes If I_0 be moment inertia of a body about an axis (AB) passing through its center of mass then moment of inertia about any axis which is parallel to AB and at a distance & from AB is I = I_0 + md^2 where m is the mass of the body Given: A thin rod of mass m_r = 7.28 kg and length L = 5.64 m is attached to a uniform sphere of mass m_s = 36.4 kg and Radius R = 1.4m m_s = 5m_r and L = 4R Since we know moment of inertia of the rod about an axis passing through it's centre of mass is (I_0)_r = m_rL^2/12 therefore MOI about AB is I_r = (I_0)_r + m_r(L/2)^2 = m_rL^2/12 + m_rL^2/4 = m_r L^2/3 MOI of a sphere about an axis