Results 1 to 7 of 7

Math Help - Radian problem please help me...

  1. #1
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381

    Radian problem please help me...

    1. A wheel has a 2cm diameter. the speed of a point on its rim is 11 m/s. What is its angular speed?
    2. A horse on a merry-go-round is 7m from the center and travels at 10km/h. What is its angular speed?
    3. A water wheel has a 10ft radius. The wheel revolves 16 times per minute. What is the speed of the river in mi/hr?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Does angular speed mean how many degrees difference it turns in a second?

    (for example, let's call the beginning point A the point after one second C and the center of the circle B... Are you trying to find angle ABC?)

    This is my 600th post!!!!
    Last edited by Quick; September 1st 2006 at 06:57 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,211
    Thanks
    419
    Awards
    1
    Quote Originally Posted by ^_^Engineer_Adam^_^
    1. A wheel has a 2cm diameter. the speed of a point on its rim is 11 m/s. What is its angular speed?
    2. A horse on a merry-go-round is 7m from the center and travels at 10km/h. What is its angular speed?
    3. A water wheel has a 10ft radius. The wheel revolves 16 times per minute. What is the speed of the river in mi/hr?
    All three of these involve the formula v = r \omega, where v is the tangential speed, r is the radius of the motion, and \omega is the angular speed.

    1. r = 1 cm = 0.01 m (NOT 2 cm!), v = 11 m/s (ALWAYS check your units!)
    So \omega = \frac{v}{r} = \frac{11}{0.01} rad/s = 1100 rad/s.

    The other two are similar. Be careful of the last one...there are a number of unit changes you need to make. My suggestion is to get the speed of the river in ft/s, then convert to mi/hr. Also to find the angular speed in problem 3, note that 16 revolutions is equal to 16 \cdot 2 \pi rad.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,211
    Thanks
    419
    Awards
    1
    Quote Originally Posted by Quick
    Does angular speed mean how many degrees difference it turns in a second?

    (for example, let's call the beginning point A the point after one second C and the center of the circle B... Are you trying to find angle ABC?)
    The angular speed is the time rate of change of the angle an object turns through. Similar to the definition of speed: v = \frac{ \Delta x}{ \Delta t} angular speed is \omega = \frac{ \Delta \theta}{ \Delta t} where \theta represents the "angular position" of the rotating object.

    Oh, and in case the units are obscure to you, 1 radian is defined as the angle marking out an arc length on a circle equal to the radius. We may calculate from this definition that \pi radians are equivalent to 180 degrees.

    -Dan
    Last edited by topsquark; September 1st 2006 at 06:30 PM. Reason: Addendum
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    I would recomend trying to figure out a formula yourself (I do it all the time)

    Here's my method:

    A wheel has diameter d, therefore it's circumference is d\pi

    Now an object moves at a speed of v around the circumference...

    therefore the angular speed, \omega for the object (in degrees) is: \omega=360\left(\frac{v}{d\pi}\right)

    which can then be converted to radians: \omega=360\left(\frac{v}{d\pi}\right)\times\frac{<br />
\pi<br />
}{180}=\frac{2v}{d}=\boxed{\frac{v}{r}}
    can you figure out how I got that answer?
    Last edited by Quick; September 1st 2006 at 06:48 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,908
    Thanks
    766
    Hello, ^_^Engineer_Adam^_^!

    Here's #3 . . .


    3. A water wheel has a 10ft radius. The wheel revolves 16 times per minute.
    What is the speed of the river in mi/hr?

    The circumference of the wheel is: . C \:=\:2\pi R = 20\pi feet.

    At 16 rev/min, a point on the wheel moves: .  16 \times 20\pi = 320\pi feet per minute.

    We have: . \frac{320\pi\;\text{feet}}{1\;\text{ minute}} \cdot \frac{60\;\text{minutes}}{\text{1 hour}} \cdot \frac{\text{1 mile}}{5280\;\text{feet}} \:=\:\frac{40\pi}{11}\text{ mph}

    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381
    thanks guys!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Radian Measure and ANgles of the Cartesion question problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 16th 2011, 11:02 AM
  2. Radian measure
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 24th 2009, 04:59 PM
  3. What is a radian?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 20th 2009, 10:08 AM
  4. radian
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: July 30th 2008, 05:57 AM
  5. another problem in radian
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 26th 2007, 04:04 AM

Search Tags


/mathhelpforum @mathhelpforum