<< Chapter < Page Chapter >> Page >

Calculating the acceleration of a fishing reel

A deep-sea fisherman hooks a big fish that swims away from the boat pulling the fishing line from his fishing reel. The whole system is initially at rest and the fishing line unwinds from the reel at a radius of 4.50 cm from its axis of rotation. The reel is given an angular acceleration of 110 rad/s 2 size 12{"110""rad/s" rSup { size 8{2} } } {} for 2.00 s as seen in [link] .

(a) What is the final angular velocity of the reel?

(b) At what speed is fishing line leaving the reel after 2.00 s elapses?

(c) How many revolutions does the reel make?

(d) How many meters of fishing line come off the reel in this time?


In each part of this example, the strategy is the same as it was for solving problems in linear kinematics. In particular, known values are identified and a relationship is then sought that can be used to solve for the unknown.

Solution for (a)

Here α size 12{α} {} and t size 12{α} {} are given and ω size 12{ω} {} needs to be determined. The most straightforward equation to use is ω = ω 0 + αt size 12{ω=ω rSub { size 8{0} } +αt} {} because the unknown is already on one side and all other terms are known. That equation states that

ω = ω 0 + αt . size 12{ω=ω rSub { size 8{0} } +αt"."} {}

We are also given that ω 0 = 0 size 12{ω rSub { size 8{0} } =0} {} (it starts from rest), so that

ω = 0 + 110 rad/s 2 2 . 00 s = 220 rad/s . size 12{ω=0+ left ("110"" rad/s" rSup { size 8{2} } right ) left (2 "." "00"" s" right )="220 rad/s."} {}

Solution for (b)

Now that ω size 12{ω} {} is known, the speed v size 12{v} {} can most easily be found using the relationship

v = , size 12{v=rω","} {}

where the radius r size 12{α} {} of the reel is given to be 4.50 cm; thus,

v = 0 . 0450 m 220 rad/s = 9 . 90 m/s. size 12{v= left (0 "." "0450"" m" right ) left ("220"" rad/s" right )=9 "." "90"" m/s."} {}

Note again that radians must always be used in any calculation relating linear and angular quantities. Also, because radians are dimensionless, we have m × rad = m size 12{m times "rad"=m} {} .

Solution for (c)

Here, we are asked to find the number of revolutions. Because 1 rev = 2π rad size 12{1" rev"=2π" rad"} {} , we can find the number of revolutions by finding θ size 12{θ} {} in radians. We are given α size 12{α} {} and t size 12{t} {} , and we know ω 0 size 12{ω rSub { size 8{ {} rSub { size 6{0} } } } } {} is zero, so that θ size 12{θ} {} can be obtained using θ = ω 0 t + 1 2 αt 2 size 12{θ=ω rSub { size 8{0} } t+ { {1} over {2} } αt rSup { size 8{2} } } {} .

θ = ω 0 t + 1 2 αt 2 = 0 + 0.500 110 rad/s 2 2.00 s 2 = 220 rad . alignl { stack { size 12{θ=ω rSub { size 8{0} } t+ { {1} over {2} } αt rSup { size 8{2} } } {} #" "=0+ left (0 "." "500" right ) left ("110"" rad/s" rSup { size 8{2} } right ) left (2 "." "00"" s" right ) rSup { size 8{2} } ="220"" rad" {} } } {}

Converting radians to revolutions gives

θ = 220 rad 1 rev 2π rad = 35.0 rev. size 12{θ= left ("220"" rad" right ) { {1" rev"} over {2π" rad"} } ="35" "." 0" rev."} {}

Solution for (d)

The number of meters of fishing line is x size 12{x} {} , which can be obtained through its relationship with θ size 12{θ} {} :

x = = 0.0450 m 220 rad = 9.90 m . size 12{x=rθ= left (0 "." "0450"" m" right ) left ("220"" rad" right )=9 "." "90"" m"} {}


This example illustrates that relationships among rotational quantities are highly analogous to those among linear quantities. We also see in this example how linear and rotational quantities are connected. The answers to the questions are realistic. After unwinding for two seconds, the reel is found to spin at 220 rad/s, which is 2100 rpm. (No wonder reels sometimes make high-pitched sounds.) The amount of fishing line played out is 9.90 m, about right for when the big fish bites.

The figure shows a fishing reel, with radius equal to 4.5 centimeters. The direction of rotation of the reel is counterclockwise. The rotational quantities are theta, omega and alpha, and x, v, a are linear or translational quantities. The reel, fishing line, and the direction of motion have been separately indicated by curved arrows pointing toward those parts.
Fishing line coming off a rotating reel moves linearly. [link] and [link] consider relationships between rotational and linear quantities associated with a fishing reel.

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 size 12{"300"`"rad/s" rSup { size 8{2} } } {} . How long does it take the reel to come to a stop?


We are asked to find the time t size 12{α} {} 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 size 12{ω rSub { size 8{0} } ="220"" rad/s"} {} and the final angular velocity ω size 12{ω} {} is zero. The angular acceleration is given to be α = 300 rad/s 2 size 12{α= - "300" "rad/s" rSup { size 8{2} } } {} . Examining the available equations, we see all quantities but t are known in ω = ω 0 + αt , size 12{ω=ω rSub { size 8{0} } +αt} {} making it easiest to use this equation.


The equation states

ω = ω 0 + αt . size 12{ω=ω rSub { size 8{0} } +αt"."} {}

We solve the equation algebraically for t , and then substitute the known values as usual, yielding

t = ω ω 0 α = 0 220 rad/s 300 rad/s 2 = 0 . 733 s. size 12{t= { {ω - ω rSub { size 8{0} } } over {α} } = { {0 - "220"" rad/s"} over { - "300""rad/s" rSup { size 8{2} } } } =0 "." "733"" s."} {}


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.

Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where is the latest information on a no technology how can I find it
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
How we can toraidal magnetic field
Aditya Reply
How we can create polaidal magnetic field
Mykayuh Reply
Because I'm writing a report and I would like to be really precise for the references
Gre Reply
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!
Gre Reply
Practice Key Terms 1

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now

Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics 101' conversation and receive update notifications?