Calculate angular speed.?

Question

The spool of a fishing rod is free to rotate since the drag wasnt set. Suddenly, a fish pulls on the line with tension T . Explain why angular momentum is not conserved.

If the spool initially set at rest has aradius of R and a moment of inertia I, what is its angular speed after a time T.

Answer 1

1. The angular momentum is not conserved because an external force is acting upon the fishing reel.

2. First off, you're trying to use T for both time and tension. I'll use smaller case t for time. τ is the torque made on the wheel, which is equal to r × T, or r T sin (Θ). Assuming Θ = 90 degrees, the torque is r T.

So we know τ = I α = r T, so α = (r T) / I (angular acceleration). Assuming the system is at rest at time t=0, we know that ω = α t. So:

ω = (r T t) / I