In 9.2 s a fisherman winds 2.1 m of fishing line onto a reel whose radius is 3.0 cm (assumed to be constant as an approximation). The line is being reeled in at a constant speed. Determine the angular speed of the reel.
7.61 rad/s
To determine the angular speed of the reel, we need to find the linear speed of the fishing line first. The linear speed is the rate at which the fishing line is being reeled in.
We are given that in 9.2 seconds, 2.1 meters of fishing line is being reeled in. We can use this information to find the linear speed.
Linear speed (v) = distance (d) / time (t)
Substituting the values given:
v = 2.1 m / 9.2 s
v ≈ 0.228 m/s
Now that we have the linear speed, we can calculate the angular speed using the formula:
Angular speed (ω) = linear speed / radius
Substituting the values:
ω = 0.228 m/s / 0.03 m
ω ≈ 7.6 rad/s
Therefore, the angular speed of the reel is approximately 7.6 rad/s.