Momentum = (mass) x (speed)
Momentum = (12,000 kg) x (40 m/s)
Momentum = (12,000 x 40) kg-m/s
<em>Momentum = 480,000 kg-m/s </em>
Answer:
New angular speed changes from 16 rpm to 19.95 rpm
Explanation:
In the given system the angular momentum of the system is conserved
initial angular momentum of the system
![L_{i}=I_{1}\omega _{1}\\\\\omega _{1}=\frac{8\pi }{15}rad/sec\\\\I_{1}=\frac{1}{2}mr^{2}+(m_{1}+m_{2}+m_{3})r^{2}\\\\I_{1}=\frac{1}{2}\times 105\times 1.8^{2}+(33+28+28) \times 1.8^{2}=458.46kgm^{2}\\\\\therefore L_{i}=458.46\times \frac{8\pi }{15}=768.16](https://tex.z-dn.net/?f=L_%7Bi%7D%3DI_%7B1%7D%5Comega%20_%7B1%7D%5C%5C%5C%5C%5Comega%20_%7B1%7D%3D%5Cfrac%7B8%5Cpi%20%7D%7B15%7Drad%2Fsec%5C%5C%5C%5CI_%7B1%7D%3D%5Cfrac%7B1%7D%7B2%7Dmr%5E%7B2%7D%2B%28m_%7B1%7D%2Bm_%7B2%7D%2Bm_%7B3%7D%29r%5E%7B2%7D%5C%5C%5C%5CI_%7B1%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20105%5Ctimes%201.8%5E%7B2%7D%2B%2833%2B28%2B28%29%20%5Ctimes%201.8%5E%7B2%7D%3D458.46kgm%5E%7B2%7D%5C%5C%5C%5C%5Ctherefore%20L_%7Bi%7D%3D458.46%5Ctimes%20%5Cfrac%7B8%5Cpi%20%7D%7B15%7D%3D768.16)
When 28 kg child moves to the center the moment of inertia changes thus we have
![I_{2}=\frac{1}{2}mr^{2}+(m_{1}+m_{2})r^{2}\\\\I_{1}=\frac{1}{2}\times 105\times 1.8^{2}+(33+28) \times 1.8^{2}=367.74kgm^{2}\\\\\therefore L_{f}=367.74\times \omega _{f}](https://tex.z-dn.net/?f=I_%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7Dmr%5E%7B2%7D%2B%28m_%7B1%7D%2Bm_%7B2%7D%29r%5E%7B2%7D%5C%5C%5C%5CI_%7B1%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20105%5Ctimes%201.8%5E%7B2%7D%2B%2833%2B28%29%20%5Ctimes%201.8%5E%7B2%7D%3D367.74kgm%5E%7B2%7D%5C%5C%5C%5C%5Ctherefore%20L_%7Bf%7D%3D367.74%5Ctimes%20%5Comega%20_%7Bf%7D)
Equating initial and final angular momentum we get
![I_{2}=\frac{1}{2}mr^{2}+(m_{1}+m_{2})r^{2}\\\\I_{1}=\frac{1}{2}\times 105\times 1.8^{2}+(33+28) \times 1.8^{2}=367.74kgm^{2}\\\\\therefore L_{f}=367.74\times \omega _{f}\\\\\omega _{f}=\frac{768.16}{367.74}=2.1rad/sec\\\\N_{2}=19.95rpm](https://tex.z-dn.net/?f=I_%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7Dmr%5E%7B2%7D%2B%28m_%7B1%7D%2Bm_%7B2%7D%29r%5E%7B2%7D%5C%5C%5C%5CI_%7B1%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20105%5Ctimes%201.8%5E%7B2%7D%2B%2833%2B28%29%20%5Ctimes%201.8%5E%7B2%7D%3D367.74kgm%5E%7B2%7D%5C%5C%5C%5C%5Ctherefore%20L_%7Bf%7D%3D367.74%5Ctimes%20%5Comega%20_%7Bf%7D%5C%5C%5C%5C%5Comega%20_%7Bf%7D%3D%5Cfrac%7B768.16%7D%7B367.74%7D%3D2.1rad%2Fsec%5C%5C%5C%5CN_%7B2%7D%3D19.95rpm)
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Answer:
A is a battery
B is a light
C is a resistor
D is a closed switch
thank you for this question, I love circuit diagrams
Explanation: