In 9.7 s a fisherman winds 2.1 m of fishing line onto a reel whose radius is 30 cm (assumed to be constant as an approximation).
The line is reeled in at constant speed.
Determine the angular speed of the reel in rad/s.
Thank you.
The velocity of pulling in the line is is
V = w * R , which means
Linear speed = (Angular speed)*(Radius)
= 2.1m/9.7s = 0.2165 m/s
Angular speed = 0.2165/0.3
= 0.7216 rad/s
r = .30 meters
2 pi r = 1.88 m
2.1/1.88 = 1.11 revolutions
1.11 * 2 pi = 7 radians
7 radians / 9.7 s = .722 rad/s
To determine the angular speed of the reel, we need to find the total angle covered by the reel in the given time period.
1. First, convert the length of fishing line wound onto the reel from meters to centimeters, since the radius of the reel is given in centimeters. We multiply 2.1 m by 100 to get 210 cm.
2. Next, we need to find the circumference of the reel using its radius. The circumference of a circle is given by the formula C = 2πr, where r is the radius. Since the radius is given as 30 cm, the circumference is calculated as C = 2 * π * 30 cm.
3. Now we can find the total number of revolutions made by the reel. We divide the length of fishing line wound onto the reel (210 cm) by the circumference of the reel (2π * 30 cm). This gives us the number of complete revolutions made by the reel.
4. To find the angular speed, we divide the total angle covered by the reel, which is the number of revolutions multiplied by 2π radians (since 1 revolution is equal to 2π radians), by the time taken (9.7 seconds). This will give us the angular speed in radians per second.
Let's plug in the values and calculate the angular speed:
Length of fishing line wound: 2.1 m = 210 cm
Radius of the reel: 30 cm
Circumference of the reel: C = 2π * 30 cm
Total revolutions made by the reel: 210 cm / (2π * 30 cm)
Angular speed: (Total revolutions made * 2π) / Time taken
Now you can calculate the angular speed using the given values.