A disk with a rotational inertia of `7.00kg*m^(2)` rotates like a merry-go-round while undergoing a variable torque given by `tau=(5.00+2.00t)N*m`. At time t = 1.00 s, its angular momentum is `5.00kg*m^(2)//s`. What is its angular momentum at t = 5.00 s?

Explanation

To find the angular momentum of the disk at time \( t = 5.00 \, \text{s} \), we will use the relationship between torque and angular momentum. The torque \( \tau \) is given by:

\[ \tau = 5.00 + 2.00t \, \text{N m} \]

We know that torque is the rate of change of angular momentum:

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