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A wheel is rotating freely at angular speed 530 rev/min on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and with 9 times the rotational inertia of the first, is suddenly coupled to the same shaft. (a) What is the angular speed of the resultant combination of the shaft and two wheels

User Emiliano Martinez
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1 Answer

26 votes
26 votes

Answer:
53\ rev/min

Step-by-step explanation:

Given

angular speed of wheel is
\omega_1 =530\ rev/min

Another wheel of 9 times the rotational inertia is coupled with initial wheel

Suppose the initial wheel has moment of inertia as I

Coupled disc has
9I as rotational inertia

Conserving angular momentum,


\Rightarrow I\omega_1=(I+9I)\omega_2\\\\\Rightarrow \omega_2=(I)/(10I)* 530\\\\\Rightarrow \omega_2=53\ rev/min

User Tacratis
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