Unknowns: T, a Gy , α Need another equation – what can I do? Kinetics (Spool rolls on Cables) α ϖ r a r a r a r r a a Gy A G G A G A A G A G A G-= × = =-× + = / 2 / 2 / / 2 2 2 2 2 2 2 2 2 2 A spool has a mass of 8 kg and a radius of gyration (k G ) of 0.35 m. Cords of negligible mass are wrapped around its inner hub and outer rim. There is no slipping. Find the angular acceleration ( α ) of the spool. ma Gx ma Gy I α G Note that I assumed all accelerations are in the positive direction – I’ll let the algebra do the work. EOM (1) (2) (3) α=-10.32 rad/s 2 T=19.77 N a Gy = 5.16 m/s 2 3 Equations and 3 Unknowns, Do the algebra! Problem Type: Find: Given: F=100 N, k G = 0.35 m, μ k = 0.2, m=8 kg, Figure α First Step? FBD, MAD!!
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