Question

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

Answer 1

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

$L_1=L_2$

$I_1\omega _1=I_2\omega _2$

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

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

$\omega _2=60\ rev/min$