Results 1 to 2 of 2

Math Help - math culminating

  1. #1
    Junior Member VDestinV's Avatar
    Joined
    May 2008
    Posts
    25

    math culminating

    A carousel at a local fall fair makes three roations in 1 min. The caraousel is 10 m in diameter. A ride lasts 5 minutes.

    a) Determine the angular velocity in rad/min and in rads.

    b) How far does a child who is riding the carousel travel in 5 minutes?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,923
    Thanks
    332
    Awards
    1
    Quote Originally Posted by VDestinV View Post
    A carousel at a local fall fair makes three roations in 1 min. The caraousel is 10 m in diameter. A ride lasts 5 minutes.

    a) Determine the angular velocity in rad/min and in rads.

    b) How far does a child who is riding the carousel travel in 5 minutes?
    I presume the last part in a) is rad/s?

    a) Angular speed is measured as "angle per time." We know it makes three revolutions (rotations) in one minute. The rest is unit conversion.
    \frac{3~revolutions}{1~min} \cdot \frac{2 \pi~rad}{1~revolution} = 6 \pi~rad/min

    Then another unit conversion:
    \frac{6 \pi~rad}{1~min} \cdot \frac{1~min}{60~s} = \frac{6 \pi~rad}{60~s} = \frac{\pi}{10}~rad/s

    Since the time is in minutes, let's use the angular speed in rad/min. We know that the angular speed is constant, so the angle swept out by the child is
    \omega = \frac{\Delta \theta}{\Delta t}

    \Delta \theta = \omega \Delta t = (6 \pi~rad/min)(5~min) = 30 \pi~rad

    Then the distance traveled will be
    \Delta s = r \Delta \theta = (5~m)(30 \pi~rad) = 150 \pi~m

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: May 29th 2011, 12:57 AM
  2. Replies: 2
    Last Post: February 14th 2011, 02:31 AM
  3. Replies: 1
    Last Post: June 19th 2010, 10:05 PM
  4. Replies: 1
    Last Post: June 2nd 2010, 09:49 AM
  5. Replies: 2
    Last Post: February 15th 2010, 03:09 PM

Search Tags


/mathhelpforum @mathhelpforum