A rod of mass 4.3 kg and length 4.3 m hangs from a hinge as shown in Figure P9.28. The end of the rod is then given a “kick” so that it is moving at a speed of 2.3 m/s. How high will the rod swing? Express your answer in terms of the angle (in degree) that the rod makes with the vertical.

Question

Hinge --> 0
i
i <-- Steel rod
i
-------> swings this way

Answer 1

w=2.3/4.3= 1 rad per second.

Now, the moment of Inertia for the rod swinging about an end is... 1/3 ml^2

initial KE= 1/2 I w^2=1/6 ml^2 figure all that out given m, l

now, final PE= mgh were h is to the center of mass. Drawing the figure, then

h+lcosTheta=lor
h= l(1-cosTheta)
finally we have
1/6ml^2=mgl(1-cosTheta)
L/6g=1-cosTheta
costheta= 1- 4.3/6g
theta= arc cos ( above)

check all this.