Some hintsThe KE's for gear B and arm OA are given by:
T_B = (1/2)*m_B*v_A^2 + (1/2)*I_A*omega_B^2
T_OA = (1/2)*I_O*omega_OA^2
with T_total = T_B + T_OA.
Same thing with potential energy. Find the potential energy for B and OA individually and add together.
The work done on the total system is:
U = +M*(pi/2)
You need KINEMATICS to relate omega_B to v_A and omega_OA to v_A. Consider the IC's for gear B and for arm OA for these relationships.
2 comments:
Is it correct to consider the mass moment of inertia of the arm OA to be m*k_o^2 and treat it more like a disk? They even give a radius of gyration, k_o, in the problem statement, which makes me think so...
Yes, you need to use I_O = m_OA*k_O^2 where k_O is the radius of gyration of OA about O. This is the definition of radius of gyration and is not so much treating the arm like a disk.
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