In 8.6 s a fisherman winds 2.7 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.

revolutions: 2.7/PI*.06

w= 2PI revolutions/8.6s in rad/sec

To determine the angular speed of the reel, we need to find the distance covered along the circumference of the reel in a given time.

First, let's convert the radius of the reel from centimeters to meters:
Radius = 3.0 cm = 0.03 m

Next, we can calculate the distance covered along the circumference of the reel:
Circumference = 2 * π * radius
Circumference = 2 * π * 0.03 m
Circumference ≈ 0.1884 m

We know that in 8.6 seconds, 2.7 meters of fishing line is winded onto the reel. Therefore, the distance covered along the circumference of the reel will be equal to the length of the fishing line.

Now, we can calculate the angular speed using the formula:
Angular Speed = Distance covered / Time

Angular Speed = 0.1884 m / 8.6 s
Angular Speed ≈ 0.0219 m/s

Therefore, the angular speed of the reel is approximately 0.0219 m/s.