Answer:
The angular speed of the record is 1.8 [tex]\frac{rad}{s}[/tex]
Explanation:
Given:
Mass [tex]m = 0.123[/tex] kg
Radius [tex]r = 0.0958[/tex] m
Angular speed [tex]\omega _{i} = 4.82 \frac{rad}{s}[/tex]
Moment of inertia [tex]I = 2.19 \times 10^{-4 }[/tex] [tex]Kg. m^{2}[/tex]
Mass of putty [tex]M = 0.0400[/tex] Kg
For finding the final angular speed,
According to the conservation of angular momentum,
[tex]L_{i} = L_{f}[/tex]
[tex](I \omega _{i} ) = (I + Mr^{2} ) \omega _{f}[/tex]
[tex]\omega _{f} = \frac{I \omega _{i} }{I + Mr^{2} }[/tex]
[tex]\omega _{f} = \frac{2.19 \times 10^{-4} \times 4.82 }{2.19 \times 10^{-4} + 0.040 \times (0.0958) ^{2} }[/tex]
[tex]\omega _{f} = 1.8 \frac{rad}{s}[/tex]
Therefore, the angular speed of the record is 1.8 [tex]\frac{rad}{s}[/tex]
