Answer:
w = [tex]\frac{m}{ml^2 + I R^2 }[/tex] v l
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 = [tex]\frac{m}{I_{total} }[/tex] 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 = [tex]\frac{m}{ml^2 + I R^2 }[/tex] v l
The angular speed f of the clay-rod system immediately after the collision
[tex]w=\dfrac{m}{ml^2+IR^2}VI[/tex]
Angular speed is defined as the rate of change of angular displacement,Angular Speed (ω) is the scalar measure of rotation rate. In one complete rotation, angular distance travelled is 2π and time is time period (T)
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
[tex]L_o=mvl[/tex]
Final moment. After the collision with the clay stuck to the rod
[tex]L_o = L_f m v l = I_{total} w[/tex]
[tex]w=\dfrac{m}{I_{total}} Vl[/tex]
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
[tex]I_rod = I R^2 I_{total} = m l^2 + IR^2[/tex]
we substitute
[tex]w=\dfrac{m}{ml^2+IR^2}VI[/tex]
Hence the angular speed f of the clay-rod system immediately after the collision
[tex]w=\dfrac{m}{ml^2+IR^2}VI[/tex]
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