Respuesta :
Answer: a) [tex]L = 10206 kg \cdot \frac{m^{2}}{s}[/tex], b) [tex]\omega_{f} = 20.25 rad/s[/tex], c) [tex]L = 10206 kg \cdot \frac{m^{2}}{s}[/tex]
Explanation:
The angular momentum of a system of particles rotating around an axis is:
[tex]L = \sum_{i=1}^{7} r_{i}^{2} \cdot m_{i} \cdot \omega[/tex]
a) The previous expression can be simplified to find the initial angular momentum:
[tex]L = 7 \cdot r^{2} \cdot m \cdot \omega\\L = 7 \cdot (9 m)^2 \cdot (2kg) \cdot (9 \frac{rad}{s} )\\L = 10206 kg \cdot \frac{m^{2}}{s}[/tex]
b) The new angular speed is calculated from the Principle of Angular Momentum Conservation, since there are no external forces influencing over the system:
[tex]L = 7 \cdot r_{f}^2 \cdot (m) \cdot \omega_{f}[/tex]
[tex]\omega_{f}=\frac{L}{7 \cdot r_{f}^2\cdot m}[/tex]
[tex]\omega_{f} = 20.25 rad/s[/tex]
c) The angular momentum remains constant, since there is no information that indicates the presence of external forces influencing the system.
(A) The initial angular momentum of the object is 10206 kgm²/s
(B) The new angular speed is 20.25 rad/s
(C) The angular momentum does not change
Conservation of angular momentum:
All 7 objects have a mass of m = 2kg. The length of the spokes is R = 9m.
(A) The angular momentum of a system is given by:
L = Iω
where I is the moment of inertia of the system
ω is the angular speed = 9 rad/s (given)
L = 7×mR²×ω
L = 7×(2×9²)×9 kgm²/s
L = 10206 kgm²/s
(B) According to the law of conservation of angular momentum, the angular momentum of the system must remain conserved.
So, the new angular momentum is:
L' = 7×(2×6²)×ω'
where ω' is the new angular momentum
10206 = 7×(2×6²)×ω'
ω' = 20.25 rad/s
(C) The new angular momentum of the object is same as the original angular momentum of the object since there is no dissipative force so the angular momentum must be conserved.
Learn more about angular momentum:
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