Question

A disk with a rotational inertia of 7.00 kg m² rotates like a merry-go-round while undergoing a torque given by τ=(5.00+2.00t) Nm. At time t = 1.00 s, its angular momentum is 5.00 kg·m²/s. What is its angular momentum at t = 3.00 s?

Answer 1

To find the angular momentum at t = 3.00 s, we need to calculate the change in angular momentum using the torque and rotational inertia. We can find the angular velocity at t = 3.00 s using the angular acceleration and initial angular velocity. Then we can calculate the angular momentum using the rotational inertia.

Step-by-step explanation:

To find the angular momentum at t = 3.00 s, we first need to find the change in angular momentum between t = 1.00 s and t = 3.00 s. The formula for angular momentum is L = Iω, where I is the rotational inertia and ω is the angular velocity.

We can find ω using the torque and the formula τ = Iα, where α is the angular acceleration. Using the given torque equation τ = (5.00 + 2.00t) Nm and integrating, we can find the angular acceleration α. Finally, we can plug in the angular acceleration and the initial angular velocity into the formula ω = ω₀ + αt to find the angular velocity at t = 3.00 s. Once we have the angular velocity, we can calculate the angular momentum using the given rotational inertia.