A uniform rod, supported and pivoted at its midpoint, but initially at rest, has

Question

A uniform rod, supported and pivoted at
its midpoint, but initially at rest, has a mass
of 84 g and a length 9 cm. A piece of clay with
mass 46 g and velocity 2.8 m/s hits the very
top of the rod, gets stuck and causes the clay-
rod system to spin about the pivot point O at
the center of the rod in a horizontal plane.
After the collisions the clay-rod system has an
angular velocity ! about the pivot.
With respect to the pivot point O, what is
the magnitude of the initial angular momen-
tum Li of the clay-rod system?
Answer in units of kgm2/s
With respect to the pivot point O, what is
the final moment of inertia If of the clay-rod
system?
Answer in units of kgm2
What is the final angular speed !f of the clay-rod
system?
Answer in units of rad/s
Answer with numbers please

Explanation / Answer

initial angular momentum of the system Li= (46/1000)*2.8*(9/200) Li = 5.796 * 10^-3 kg.m^2/s final moment of inertia I= (84/1000)*(9/100)^2/12 + (46/1000)*(9/200)^2 I = 1.4985 * 10^-4 kg.m^2 applying conservation of angular momentum intial angualr momentum = final angular momentum so, final angular momentum = 5.796 * 10^-3 kg.m^2/s so, I*w = 5.796 * 10^-3 where w-final angular velocity;I-final moment of inertia so w = 5.796 * 10^-3/(1.4985 * 10^-4) w =38.68 rad/s so,final angular velocity = 38.68 rad/s

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