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3 years ago

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A wheel is rotating freely at angular speed 420 rev/min on a shaft whose rotational inertia is negligible. A second wheel, initi

ally at rest and with 7 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

1 answer:

Mashcka [7]3 years ago

8 0

Answer:60 rev/min

Explanation:

Given

angular speed of first shaft $\omega _1=420\ rev/min$

Moment of inertia of second shaft is seven times times the rotational speed of the first i.e. If I is the moment of inertia of first wheel so moment of inertia of second is 7 I

As there is no external torque therefore angular momentum is conserved

$L_1=L_2$

$I_1\omega _1=I_2\omega _2$

$I\times (420)=7 I\times (\omega _2)$

$\omega _2=\frac{420}{7}$

$\omega _2=60\ rev/min$

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