Final answer:
To calculate the final angular speed of the system, find the total moment of inertia, then determine the torque from the applied force and use it to calculate the angular acceleration. Finally, multiply the angular acceleration by the time the force is applied to find the angular speed.
Step-by-step explanation:
The student has asked about calculating the angular speed of an apparatus composed of a uniform disk and four rods with masses at the end after a force is applied to it. Since the system is initially at rest, we need to use the principles of rotational motion to solve this problem. Due to the applied force causing rotation, we can use the formula for torque (τ = rF) and the relationship between torque and angular acceleration (α = τ/I where I is the moment of inertia), followed by the equation for angular speed (ω = α t) to find the final angular speed.
First we would need to calculate the moment of inertia for the entire apparatus, which includes the moment of inertia of the disk plus the moment of inertia of the four point masses (located at the end of the rods).
The moment of inertia for a point mass is I = mr². Then, add the contribution from each mass to find the total moment of inertia. Second, calculate the torque produced by the force, and then use the calculated torque to determine the angular acceleration. Third, knowing the angular acceleration, we can then calculate the final angular speed of the apparatus using the given time during which the force is applied. However, without completing the full calculations, a definitive answer cannot be given here.