Question

problem 3:
a person catches a fish and starts reeling the fish in. the reel accelerates with an angular acceleration of \\( \alpha = 25 rad/s^{2} \\) for a time of 1.5 s. find the total angle the reel has turned \\( (\delta\theta =?) \\).

Explanation:

Step1: Recall the angular kinematic equation

The equation for angular displacement when the initial angular velocity \(\omega_0 = 0\) (assuming the reel starts from rest) is \(\Delta\theta=\omega_0t+\frac{1}{2}\alpha t^{2}\). Since \(\omega_0 = 0\), the equation simplifies to \(\Delta\theta=\frac{1}{2}\alpha t^{2}\).

Step2: Substitute the given values

We are given \(\alpha = 25\ rad/s^{2}\) and \(t = 1.5\ s\). Substitute these values into the formula: \(\Delta\theta=\frac{1}{2}\times25\times(1.5)^{2}\).
First, calculate \((1.5)^{2}=2.25\). Then, \(\frac{1}{2}\times25\times2.25=\frac{25\times2.25}{2}\).
\(25\times2.25 = 56.25\), and \(\frac{56.25}{2}=28.125\)

Answer:

\(28.125\ rad\)