Answer:
w =
v l
Step-by-step explanation:
Let's form a system formed by the clay sphere and the rod, in this case the angular momentum is conserved
initial instant. Before the crash
L₀ = m v l
Final moment. After the collision with the clay stuck to the rod
L_f = I_{total} w
angular momentum is conserved
L₀ = L_f
m v l = I_total w
w =
v l
the total moment of inertia is the sum of the moments of inertia of the two bodies
the moment of inertia of the rod is
I_rod = I R²
I_total = m l² + IR²
we substitute
w =
v l