A long wooden rod is supported in the vertical position by a hinge/pivot at its upper end so that it is free to swing like a pendulum. The length of the rod is 2.70 m and its mass is 2.10 kg. The rod is struck by a lump of clay, whose mass is 500 g, moving horizontally and which sticks to the bottom end of the rod. This makes the rod swing out to a maximum angle of 𝜃 = 28^{o}.

**A.** How far, h_{0}, from the top of the rod is the center of mass of the rod-clay system just before the rod leaves the vertical position with the clay attached?

h_{0} = m

**B.** When the system has swung to ^{o}, how high, Δh,has the center of mass moved from its original position?

[Suggestion: Draw a before and after diagram of the rod and used trigonometry.]

Δh = m

**C.** What is the system's increase in potential energy?

[Hint: Would knowing about the center of mass's motion help?]

ΔU = J

**D.** What is the moment of inertia of the rod-clay system? The rod is pivoting about its upper end and the clay is a point mass. I = I_{rod} + I_{clay}

[Suggestion: Look up the expression for the moment of inertia of the rod pivoting at one end.]

I = kg m^{2}

**E.** Using conservation of mechanical energy, what is the initial kinetic energy, angular speed and angular momentum of the rod-clay system (before it leaves the vertical position)?

K_{0} = J

𝜔 = rad/s

L_{0} = kg m^{2}/s

**F.** If the clay's initial angular momentum before striking the rod was *m*_{clay}·*L*_{rod}·*v*_{clay}

, what was the clay's speed before striking the rod?

v = m/s