Facebook Page
Twitter
RSS
+ Reply to Thread
Results 1 to 6 of 6
  1. MHB Apprentice

    Status
    Offline
    Join Date
    Nov 2016
    Posts
    5
    Thanks
    2 times
    Thanked
    1 time
    #1
    Hello all! I need help with a certain type of problem. I do not know how I can find the diameter of a circular object given it's linear velocity. Here is an example problem, and I would love any explanation you could give me! Thanks! )

    Leaving the Ferris Wheel, Daniel sees his friend, Jenna, riding the Super Circle Swings. As he watches, she goes around 10 times in one minute. The sign on the ride claims that the swings travel 19mph. What is the diameter of the ride if the sign is correct?
    Last edited by fluffertoes; November 25th, 2016 at 23:30.

  2. MHB Journeyman
    MHB Math Helper
    topsquark's Avatar
    Status
    Offline
    Join Date
    Aug 2012
    Location
    The Astral plane
    Posts
    735
    Thanks
    3,770 times
    Thanked
    1,554 time
    Thank/Post
    2.114
    Awards
    MHB Humor Award (2016)  

MHB Humor Award (2015)  

MHB Humor Award (2014)
    #2
    Quote Originally Posted by fluffertoes View Post
    Hello all! I need help with a certain type of problem. I do not know how I can find the diameter of a circular object given it's linear velocity. Here is an example problem, and I would love any explanation you could give me! Thanks! )

    Leaving the Ferris Wheel, Daniel sees his friend, Jenna, riding the Super Circle Swings. As he watches, she goes around 10 times in one minute. The sign on the ride claims that the swings travel 19mph. What is the diameter of the ride if the sign is correct?
    Hint: $ \displaystyle v = \omega r$

    How do you find $ \displaystyle \omega$ ? I'd advised changing the 19 mi/h to ft/min.

    -Dan

  3. MHB Seeker
    MHB Global Moderator
    MHB Math Scholar
    I like Serena's Avatar
    Status
    Offline
    Join Date
    Mar 2012
    Location
    Netherlands
    Posts
    5,925
    Thanks
    3,995 times
    Thanked
    11,236 times
    Thank/Post
    1.896
    Awards
    MHB Model Helper Award (2016)  

MHB Best Ideas (2016)  

MHB LaTeX Award (2016)  

MHB Calculus Award (2014)  

MHB Discrete Mathematics Award (Jul-Dec 2013)
    #3
    Quote Originally Posted by topsquark View Post
    Hint: $ \displaystyle v = \omega r$

    How do you find $ \displaystyle \omega$ ? I'd advised changing the 19 mi/h to ft/min.

    -Dan
    Oh my, are people ever going to switch to a system, not necessarily the metric system, that doesn't require a factor or divisor of, say, 88?

  4. MHB Apprentice

    Status
    Offline
    Join Date
    Nov 2016
    Posts
    5
    Thanks
    2 times
    Thanked
    1 time
    #4 Thread Author
    Quote Originally Posted by I like Serena View Post
    Oh my, are people ever going to switch to a system, not necessarily the metric system, that doesn't require a factor or divisor of, say, 88?
    I really just don't know what to do....

  5. Pessimist Singularitarian
    MHB Coder
    MHB Math Helper
    MHB Ambassador
    MarkFL's Avatar
    Status
    Offline
    Join Date
    Feb 2012
    Location
    St. Augustine, FL.
    Posts
    10,990
    Thanks
    31,354 times
    Thanked
    26,189 times
    Thank/Post
    2.383
    Trophies
    20 Highscores
    Awards
    MHB Statistics Award (2016)  

MHB Calculus Award (2016)  

MHB Pre-University Math Award (2016)  

MHB Model Helper Award (2015)  

MHB Calculus Award (2015)
    #5
    Let's begin by taking the formula Dan provided, and solve for $r$:

    $ \displaystyle r=\frac{v}{\omega}$

    Now, we know the radius $r$ is half the diameter $d$:

    $ \displaystyle d=\frac{2v}{\omega}$

    We are given:

    $ \displaystyle v=19\text{ mph}\cdot\frac{5280\text{ ft}}{1\text{ mi}}\cdot\frac{1\text{ hr}}{60\text{ min}}=1672\,\frac{\text{ft}}{\text{min}}$

    Now we need to turn 10 revolutions per minutes into an angular velocity given in radians (dimensionless) per minute:

    $ \displaystyle \omega=10\,\frac{\text{rev}}{\text{min}}\cdot\frac{2\pi}{1\text{ rev}}=20\pi\,\frac{1}{\text{min}}$

    So, plug in these values...what do you get for $d$?

  6. MHB Journeyman
    MHB Math Helper
    topsquark's Avatar
    Status
    Offline
    Join Date
    Aug 2012
    Location
    The Astral plane
    Posts
    735
    Thanks
    3,770 times
    Thanked
    1,554 time
    Thank/Post
    2.114
    Awards
    MHB Humor Award (2016)  

MHB Humor Award (2015)  

MHB Humor Award (2014)
    #6
    Quote Originally Posted by I like Serena View Post
    Oh my, are people ever going to switch to a system, not necessarily the metric system, that doesn't require a factor or divisor of, say, 88?
    Hey, you're preaching to the choir. But, given the units, I figure the answer will be in ft.

    -Dan

Similar Threads

  1. Replies: 2
    Last Post: May 23rd, 2014, 20:39
  2. Replies: 3
    Last Post: May 21st, 2014, 16:10
  3. Group Velocity and Phase Velocity
    By Joystar1977 in forum Other Advanced Topics
    Replies: 1
    Last Post: January 28th, 2014, 16:06
  4. [SOLVED] linear and angular velocity of 2 pulleys and a belt.
    By karush in forum Trigonometry
    Replies: 1
    Last Post: October 8th, 2013, 22:36
  5. Find the radius of a circle.
    By anemone in forum Challenge Questions and Puzzles
    Replies: 4
    Last Post: April 23rd, 2013, 14:18

Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
Math Help Boards