Final answer:
To find the angular speed of the combination of two rotating cylinders when coupled, we use the conservation of angular momentum. The angular speed of the combination is 3.0 rad/s and the percentage of the original kinetic energy lost to friction is 40%. Thus (option A) is right answer.
Step-by-step explanation:
To find the angular speed of the combination, we can use the conservation of angular momentum. Since the cylinders couple and rotate about the same axis, the total angular momentum before and after the coupling remains the same. Angular momentum is given by the product of moment of inertia and angular velocity. The moment of inertia of the combination can be calculated as the sum of the moment of inertia of the individual cylinders. By setting the initial and final angular momentum equal to each other, we can solve for the angular speed of the combination.
The initial kinetic energy of the system can be calculated as the sum of the kinetic energy of the two cylinders. The kinetic energy lost to friction is the difference between the initial kinetic energy and the final kinetic energy of the combination.
We can calculate the final kinetic energy using the formula 1/2 * I_total * ω_combination^2, where I_total is the total moment of inertia and ω_combination is the angular speed of the combination.
By dividing the kinetic energy lost to friction by the initial kinetic energy and multiplying by 100%, we can find the percentage of kinetic energy lost to friction.
The angular speed of the combination is 3.0 rad/s.
The percentage of the original kinetic energy lost to friction is 40%.
Thus (option A) is right answer.