Calculating the Duration When the Fishing Reel Slows Down and Stops · Physics Playground

Example 10.4 from College Physics, 10.2 Kinematics of Rotational Motion

Calculating the Duration When the Fishing Reel Slows Down and Stops

Now let us consider what happens if the fisherman applies a brake to the spinning reel, achieving an angular acceleration of $- 300 {rad/s}^{2}$ . How long does it take the reel to come to a stop?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We are asked to find the time $t$ for the reel to come to a stop. The initial and final conditions are different from those in the previous problem, which involved the same fishing reel. Now we see that the initial angular velocity is $ω_{0} = 220 rad/s$ and the final angular velocity $ω$ is zero. The angular acceleration is given to be $α = - 300 {rad/s}^{2}$ . Examining the available equations, we see all quantities but t are known in $ω = ω_{0} + αt,$ making it easiest to use this equation.
Solution
The equation states

$ω = ω_{0} + αt .$
10.28

We solve the equation algebraically for t, and then substitute the known values as usual, yielding
$t = \frac{ω - ω_{0}}{α} = \frac{0 - 220 rad/s}{- 300 {rad/s}^{2}} = 0 . 733 s.$
10.29
Discussion
Note that care must be taken with the signs that indicate the directions of various quantities. Also, note that the time to stop the reel is fairly small because the acceleration is rather large. Fishing lines sometimes snap because of the accelerations involved, and fishermen often let the fish swim for a while before applying brakes on the reel. A tired fish will be slower, requiring a smaller acceleration.

0 of 3 steps open

How did it go?

Strategy

Solution

Discussion