Final answer:
The angular momentum acquired by the top can be calculated using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. The moment of inertia for a top can be approximated as that of a solid cylinder with the axis of rotation passing through its center. Plugging in the given values, the angular momentum acquired by the top is 7.66×10^-8 kg.m²/s.
Step-by-step explanation:
To find the angular momentum acquired by the top, we need to calculate the angular velocity first. We know that the tension in each string is 2.40 N and the time taken for the string to unwind is 0.560 s. The torque acting on the top is equal to the tension multiplied by the radius of the axle, which is 2.46 mm or 0.00246 m. Using the torque formula τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration, we can rearrange the formula to solve for α. Then, using the equation ω = ω₀ + αt, where ω is the angular velocity, ω₀ is the initial angular velocity (0 in this case since the top starts at rest), α is the angular acceleration, and t is the time, we can find the angular velocity.
Now that we have the angular velocity, we can calculate the angular momentum using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. The moment of inertia for a top can be approximated as that of a solid cylinder with the axis of rotation passing through its center, which is given by I = 0.5mr², where m is the total mass of the top and r is the radius of the axle.
Plugging in the values we have, the moment of inertia is 0.5 × (2.40×10^-3 kg) × (2.46×10^-3 m)² = 6.13 ×10^-9 kg.m². Substituting this value and the angular velocity into the formula for angular momentum, we get L = 6.13×10^-9 kg.m² × (12.50 rad/s) = 7.66×10^-8 kg.m²/s.