Gears A and B of mass 10 kg and 50 kg have radii of gyration about their respective mass

Chapter 19, Problem F19-4

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QUESTION:

Gears A and B of mass 10 kg and 50 kg have radii of gyration about their respective mass centers of \(k_{A} = 80 \ mm\) and \(k_{B} = 150 \ mm\). If gear A is subjected to the couple moment \(M = 10 \ N \cdot m\) when it is at rest, determine the angular velocity of gear B when t = 5 s.

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QUESTION:

Gears A and B of mass 10 kg and 50 kg have radii of gyration about their respective mass centers of \(k_{A} = 80 \ mm\) and \(k_{B} = 150 \ mm\). If gear A is subjected to the couple moment \(M = 10 \ N \cdot m\) when it is at rest, determine the angular velocity of gear B when t = 5 s.

ANSWER:

Problem F19-4

Gears A and B of mass 10 kg and 50 kg have radii of gyration about their respective mass centers of  = 80 mm and  = 150 mm. If gear A is subjected to the couple moment M = 10 N  m when it is at rest, determine the angular velocity of gear B when t 5 s.

                                                               Step by Step Solution

Step 1 of 3

Applying the principle of angular impulse and momentum about A

As we know that,

           (1)

Where M  = couple moment =

 Mass of gear

 Radius of gyration of gear

 angular velocity of gear A

 Time = 5 sec

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