Answer:1.7 rev/s
Explanation:
Given
Frequency of wheel [tex]N_1=2\ rev/s[/tex]
angular speed [tex]\omega_1=2\pi N_1=4\pi\ rad/s[/tex]
mass of wheel [tex]m_1=4.5\ kg[/tex]
diameter of wheel [tex]d_1=0.30\ m=30\ cm[/tex]
radius of wheel [tex]r_1=\frac{d_1}{2}=\frac{30}{2}=15\ cm[/tex]
mass of clay [tex]m_2=2.8\ kg[/tex]
the radius of the chunk of clay [tex]r_2=8\ cm[/tex]
Moment of inertia of Wheel
[tex]I_1=\dfrac{m_1r_1^2}{2}=\dfrac{4.5\times 15^2}{2}\ kg-cm^2[/tex]
Combined moment of inertia of wheel and clay chunk
[tex]I_2=\dfrac{m_1r_1^2}{2}+\dfrac{m_2r_2^2}{2}=\dfrac{4.5\times 15^2}{2}+\dfrac{2.8\times 8^2}{2}\ kg-cm^2[/tex]
Conserving angular momentum
[tex]\Rightarrow I_1\omega_1=I_2\omega_2\\\Rightarrow \dfrac{4.5\times 15^2}{2}\cdot 4\pi=(\dfrac{4.5\times 15^2}{2}+\dfrac{2.8\times 8^2}{2})\omega_2\\\\\Rightarrow \omega _2=\dfrac{4\pi }{1+\dfrac{2.8}{4.5}\times (\dfrac{8}{15})^2}=\dfrac{4\pi}{1+0.1769}=0.849\times 4\pi[/tex]
Common frequency of wheel and chunk of clay is
[tex]\Rightarrow N_2=\dfrac{4\pi \times 0.849}{2\pi}=1.698\approx 1.7\ rev/s[/tex]
