A rod is bent into an L shape and attached at one point to a pivot. (Figure 1) The rod sits on a frictionless?

Question

A rod is bent into an L shape and attached at one point to a pivot (see Figure 1). The rod rests on a frictionless table, and the diagram is viewed from above. For this problem, gravity can be ignored. Three forces are applied to the rod at different points and angles: F₁, F₂, and F₃. The dimensions of the bent rod are given in centimeters in the figure, but the answers should be provided in SI units (kilograms, meters, seconds).
Part A: If F₃ = 0 and F₁ = 12 N, what must the magnitude of F₂ be for the rod to achieve rotational equilibrium? I have calculated F₂, and it is correct: F₂ = 4.5 N.
Part B: If the L-shaped rod has a moment of inertia I = 9 kg·m², F₁ = 12 N, F₂ = 27 N, and F₃ = 0, how long will it take for the object to rotate through 45° (π/4 radians)? Please express the time t in seconds. Assume that as the object begins to move, each force maintains its initial angle relative to the object.
Part C: Now consider the scenario where F₁ = 12 N and F₂ = 0, but a force with a nonzero magnitude, F₃, is acting on the rod. What must the magnitude of F₃ be to achieve equilibrium? Provide a numerical answer in newtons, to two significant figures. F₃ = 
Please express the time in seconds to two significant figures.

Anonymous · Accepted Answer

B) τ = 12N3cm - 27N8cm = -180 N·cm = -1.8 N·m
But also τ = Iα, so
α = -1.8N·m / 9kg·m² = -0.2 rad/s²
Θ = ½αt²
π/4 rads = ½  0.2rad/s²  t² → t = 2.8 s
C) 12N  3cm = F3  sin30 * 8cm
F3 = 9.0 N

Yolanda Torp Sr.

A rod is bent into an L shape and attached at one point to a pivot. (Figure 1) The rod sits on a frictionless?

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