Two astronauts, each with a mass of 50 kg, are connected by a 7 m massless rope. Initially they are rotating around their center of mass with an angular velocity of 0.5 rad/s. One of the astronauts then pulls on the rope shortening the distance between the two astronauts to 4 m. What was the averageangular speed exerted by the astronaut on the rope?

The angular  velocity is

Explanation:

From the question we are told that

     The mass of each astronauts is  

      The initial  distance between the two  astronauts  

Generally the radius is mathematically represented as

      The initial  angular velocity is  

       The  distance between the two astronauts after the rope is pulled is

Generally the radius is mathematically represented as

Generally from the law of angular momentum conservation we have that

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

Also   is the initial angular velocity of the first astronauts which is equal to the initial angular velocity of the second astronauts  So

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

Also   is the final angular velocity of the first astronauts which is equal to the  final angular velocity of the second astronauts  So

So

=>  

=>  

=>    

=>  

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