Answer:
True
Explanation:
An independent variable is the variable that is changed or controlled in a scientific experiment to test the effects on the dependent variable. You are changing light or dark
the SL unit of acceleration is the meter per second squared
Twenty is the atomic number of potassium.
Answer:
The angular velocity is ![w_f = 1.531 \ rad/ s](https://tex.z-dn.net/?f=w_f%20%3D%20%201.531%20%5C%20rad%2F%20s)
Explanation:
From the question we are told that
The mass of each astronauts is ![m = 50 \ kg](https://tex.z-dn.net/?f=m%20%3D%20%2050%20%5C%20kg)
The initial distance between the two astronauts ![d_i = 7 \ m](https://tex.z-dn.net/?f=d_i%20%20%3D%20%207%20%5C%20%20m)
Generally the radius is mathematically represented as ![r_i = \frac{d_i}{2} = \frac{7}{2} = 3.5 \ m](https://tex.z-dn.net/?f=r_i%20%20%3D%20%20%5Cfrac%7Bd_i%7D%7B2%7D%20%3D%20%5Cfrac%7B7%7D%7B2%7D%20%20%3D%20%203.5%20%5C%20%20m)
The initial angular velocity is ![w_1 = 0.5 \ rad /s](https://tex.z-dn.net/?f=w_1%20%3D%200.5%20%5C%20%20rad%20%2Fs)
The distance between the two astronauts after the rope is pulled is ![d_f = 4 \ m](https://tex.z-dn.net/?f=d_f%20%3D%20%204%20%5C%20%20m)
Generally the radius is mathematically represented as ![r_f = \frac{d_f}{2} = \frac{4}{2} = 2\ m](https://tex.z-dn.net/?f=r_f%20%20%3D%20%20%5Cfrac%7Bd_f%7D%7B2%7D%20%3D%20%5Cfrac%7B4%7D%7B2%7D%20%20%3D%20%202%5C%20%20m)
Generally from the law of angular momentum conservation we have that
![I_{k_1} w_{k_1}+ I_{p_1} w_{p_1} = I_{k_2} w_{k_2}+ I_{p_2} w_{p_2}](https://tex.z-dn.net/?f=I_%7Bk_1%7D%20w_%7Bk_1%7D%2B%20I_%7Bp_1%7D%20w_%7Bp_1%7D%20%3D%20I_%7Bk_2%7D%20w_%7Bk_2%7D%2B%20I_%7Bp_2%7D%20w_%7Bp_2%7D)
Here
is the initial moment of inertia of the first astronauts which is equal to
the initial moment of inertia of the second astronauts So
![I_{k_1} = I_{p_1 } = m * r_i^2](https://tex.z-dn.net/?f=I_%7Bk_1%7D%20%3D%20I_%7Bp_1%20%7D%20%3D%20%20m%20%2A%20%20r_i%5E2)
Also
is the initial angular velocity of the first astronauts which is equal to
the initial angular velocity of the second astronauts So
![w_{k_1} =w_{p_1 } = w_1](https://tex.z-dn.net/?f=w_%7Bk_1%7D%20%3Dw_%7Bp_1%20%7D%20%3D%20w_1)
Here
is the final moment of inertia of the first astronauts which is equal to
the final moment of inertia of the second astronauts So
![I_{k_2} = I_{p_2} = m * r_f^2](https://tex.z-dn.net/?f=I_%7Bk_2%7D%20%3D%20I_%7Bp_2%7D%20%3D%20%20m%20%2A%20%20r_f%5E2)
Also
is the final angular velocity of the first astronauts which is equal to
the final angular velocity of the second astronauts So
![w_{k_2} =w_{p_2 } = w_2](https://tex.z-dn.net/?f=w_%7Bk_2%7D%20%3Dw_%7Bp_2%20%7D%20%3D%20w_2)
So
![mr_i^2 w_1 + mr_i^2 w_1 = mr_f^2 w_2 + mr_f^2 w_2](https://tex.z-dn.net/?f=mr_i%5E2%20w_1%20%2B%20mr_i%5E2%20w_1%20%3D%20mr_f%5E2%20w_2%20%2B%20mr_f%5E2%20w_2)
=> ![2 mr_i^2 w_1 = 2 mr_f^2 w_2](https://tex.z-dn.net/?f=2%20mr_i%5E2%20w_1%20%3D%202%20mr_f%5E2%20w_2)
=> ![w_f = \frac{2 * m * r_i^2 w_1}{2 * m * r_f^2 }](https://tex.z-dn.net/?f=w_f%20%3D%20%20%5Cfrac%7B2%20%2A%20m%20%2A%20r_i%5E2%20w_1%7D%7B2%20%2A%20m%20%2A%20%20r_f%5E2%20%7D)
=> ![w_f = \frac{3.5^2 * 0.5}{ 2^2 }](https://tex.z-dn.net/?f=w_f%20%3D%20%20%5Cfrac%7B3.5%5E2%20%2A%20%200.5%7D%7B%20%202%5E2%20%7D)
=> ![w_f = 1.531 \ rad/ s](https://tex.z-dn.net/?f=w_f%20%3D%20%201.531%20%5C%20rad%2F%20s)
The speed is 0.2 meter per minute.
There is not enough information given in the question to determine the velocity.