Results 1 to 7 of 7

Math Help - Linear and angular velocity 2 problems?

  1. #1
    Senior Member
    Joined
    Dec 2010
    From
    CPT
    Posts
    302

    Linear and angular velocity 2 problems?

    My first problem is change 85 radians per second to revolutions per minute I know you have to use dimensional analysis.
    So would It be
    85 rad I am not sure how to set up the rest
    -------=
    1 sec

    My second problem is this find the linear velocity in millimeters per second for each hand which is 30 millimeters long
    I know the formula is v=r(angular velocity)
    I know r= 30 but I am unsure how to find angular velocity
    Can anyone help me with these two problems?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by homeylova223 View Post
    My first problem is change 85 radians per second to revolutions per minute I know you have to use dimensional analysis.
    So would It be
    85 rad I am not sure how to set up the rest
    -------=
    1 sec

    My second problem is this find the linear velocity in millimeters per second for each hand which is 30 millimeters long
    I know the formula is v=r(angular velocity)
    I know r= 30 but I am unsure how to find angular velocity
    Can anyone help me with these two problems?
    \displaystyle 85 \, \frac{rad}{sec} \cdot \frac{60 \, sec}{1 \, min} \cdot \frac{1 \, rev}{2\pi \, rad}


    second problem ... what do you mean by "each hand" ? hands of a clock?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,659
    Thanks
    600
    Hello, homeylova223!

    I'll baby-step through the procedure . . .


    My first problem is change 85 radians per second to revolutions per minute.

    You started correctly.

    \text{We have: }\:\dfrac{85\text{ rad}}{1\text{ sec}}\;\hdots\text{ and we want: }\:\dfrac{x\text{ rev}}{1\text{ min}}

    Our game plan: replace "rad" with "rev", and replace "sec" with "min".




    We want to change radians to revolutions.

    We know that: . 1\text{ rev} \:=\:2\pi\text{ rad}

    Form a fraction with the two equivalent quantities.
    . . \text{There are two possible fractions: }\:\dfrac{2\pi\text{ rad}}{1\text{ rev}} \,\text{ or }\,\dfrac{1\text{ rev}}{2\pi\text{ rad}}


    Choose the fraction that will cancel the "rads", and multiply.

    . . \displaystyle \frac{85\,\rlap{///}\text{rad}}{1\,\text{sec}} \times \frac{1\,\text{rev}}{2\pi\,\rlap{///}\text{rad}} \;=\;\frac{85\,\text{rev}}{2\pi\,\text{sec}}


    We want to change "sec" to "min".

    We know that: . 60\text{ sec} \,=\,1\text{ min}.

    Form a fraction with the two equivalent quantities.
    . . There are two possible fractions: . \dfrac{60\text{ sec}}{1\text{ min}}\,\text{ or }\,\dfrac{1\text{ min}}{60\text{ sec}}

    Choose the fraction that will cancel the "secs", and multiply.

    . . \displaystyle \frac{85\,\text{rev}}{2\pi\,\rlap{///}\text{sec}} \times \frac{60\,\rlap{///}\text{sec}}{1\,\text{min}} \;=\; \frac{2550\text{ rev}}{\pi\text{ min}}


    Therefore: . 85\text{ rad/sec} \;\approx\;811.7\text{ rpm.}

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Dec 2010
    From
    CPT
    Posts
    302
    Yeah it is second hand on a clock I think.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by homeylova223 View Post
    Yeah it is second hand on a clock I think.
    a second hand completes 1 revolution in 1 minute ... convert that to radians per second.

    v = r\omega
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Dec 2010
    From
    CPT
    Posts
    302
    I have a quick question when I multiplied 85 rev x 60 I get 5100 do you divide by half?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by homeylova223 View Post
    I have a quick question when I multiplied 85 rev x 60 I get 5100 do you divide by half?
    no, divide by 2\pi ...

    \displaystyle \frac{85 \cdot 60}{2\pi}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Angular and linear velocity problem...
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: January 31st 2010, 08:38 AM
  2. Angular velocity
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: July 5th 2009, 05:41 AM
  3. Angular Velocity and other problems
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 11th 2009, 08:57 AM
  4. Angular Velocity and other problems
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 11th 2009, 06:50 AM
  5. Replies: 1
    Last Post: August 29th 2008, 02:18 AM

Search Tags


/mathhelpforum @mathhelpforum