A rod is bent into an L shape and attached at one point to a pivot. (Figure 1) T

Question

A rod is bent into an L shape and attached at one point to a pivot. (Figure 1) The rod sits on a frictionless table and the diagram is a view from above. This means that gravity can be ignored for this problem. There are three forces that are applied to the rod at different points and angles: F 1, F 2, and F 3. Note that the dimensions of the bent rod are in centimeters in the figure, although the answers are requested in SI units (kilograms, meters, seconds). A)If F3=0 and F1=12N, what does the magnitude of F 2 have to be for there to be rotational equilibrium?

B)If the L-shaped rod has a moment of inertia I=9kgm2, F1=12N, F2=27N, and again F3=0, how long a time t would it take for the object to move through 45 ( /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.

Explanation / Answer

a)

F2 = 4.5 N

b)

= 12N*3cm - 27N*8cm = -180 N·cm = -1.8 N·m

But also = I, so

= -1.8N·m / 9kg·m² = -0.2 rad/s²

= ½t²

/4 rads = ½ * 0.2rad/s² * t² t = 2.8 sec

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