Question

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

Answer 1

Answer: $53\ rev/min$

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,

$\Rightarrow I\omega_1=(I+9I)\omega_2\\\\\Rightarrow \omega_2=\dfrac{I}{10I}\times 530\\\\\Rightarrow \omega_2=53\ rev/min$