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QMoments around a rod

A rod is bent into an L shape and attached at one point to a pivot. The rod sits on a frictionless table and the diagram is a view from above. This means thatgravity can be ignored for this problem. There are three forces that are applied to the rod at different points and angles: F1, F2, F3 and . Note that thedimensions of the bent rod are in centimeters in the figure, although the answers are requested in SI units (kilograms, meters, seconds).

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This is the Diagram:

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Questions:

1. If F_3=0 and F_1=12\;{\rm N}, what does the magnitude of F_2_vec have to be for there to be rotational equilibrium?

________N

2.

If the L-shaped rod has a moment of inertia I=9\;{\rm kg}\; {\rm m}^2, F_1= 12\; {\rm N}, F_2= 27\; {\rm N}, andagain F_3 =0, how long a time t would it take for the object to move through45^\circ ( pi/4 radians)?

Assume that as the object starts to move, each force moves with the object so as to retain its initial angle relative to the object.

t= _________ s

3. Now consider the situation in which F_1=12\; {\rm N} and F_2=0, but now a force with nonzeromagnitude F_3 is acting on the rod. Whatdoes F_3 have to be to obtain equilibrium?

F_3= __________ N

Thank you

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