Three forces are applied to a solid cylinder of mass 12 kg (see the drawing). Th

Question

Three forces are applied to a solid cylinder of mass 12 kg (see the drawing). The magnitudes of the forces are F1 = 15 N, F2 = 24 N, and F3 = 20. N. The radial distances are R2 = 0.22 m and R3 = 0.10 m. The forces F with arrow2 and F with arrow3 are perpendicular to the radial lines labeled R2 and R3. The moment of inertia of the cylinder is 1/2 MR2^2 . Find the magnitude of the angular acceleration of the cylinder about the axis of rotation.

Three forces are applied to a solid cylinder of mass 12 kg (see the drawing). The magnitudes of the forces are F1 = 15 N, F2 = 24 N, and F3 = 20. N. The radial distances are R2 = 0.22 m and R3 = 0.10 m. The forces F with arrow2 and F with arrow3 are perpendicular to the radial lines labeled R2 and R3. The moment of inertia of the cylinder is 1/2 MR2^2 . Find the magnitude of the angular acceleration of the cylinder about the axis of rotation

Explanation / Answer

Torque Q = F2*R2 - F3*R3 = 24*0.22 - 20*0.1 = 5.28 - 2 = 3.28 N?m

I = 0.5*m*R2^2 = 0.5*12*0.22^2 = 0.2904 kg?m^2

?(alpha) = Q/I = 11.2946 rad/sec^2 CCW

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