Results 1 to 5 of 5
Like Tree2Thanks
  • 1 Post By Hartlw
  • 1 Post By HallsofIvy

Math Help - Show that v=ωr using dot product or vector products

  1. #1
    Junior Member
    Joined
    Dec 2012
    From
    china
    Posts
    30

    Show that v=ωr using dot product or vector products

    Show that v=ωr using dot product or vector products.
    anyone can teach me how to do the question below?




    Show that v=ωr using dot product or vector products-vwr.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Aug 2010
    Posts
    961
    Thanks
    98

    Re: Show that v=ωr using dot product or vector products

    v = wR = rsin(theta)w. v = wXr, (right hand rule)
    Thanks from happymatthematics
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2012
    From
    china
    Posts
    30

    Re: Show that v=ωr using dot product or vector products

    Thank you Hartlw. but I still don't understand.
    sorry to ask you more questions.
    do R has a physical meaning? I don't know why v = wR.
    also, I only learnt ||aXb||=||a||||b||sin(thetre), but didn't learn what aXb is.
    According to your reply, is aXb = b sin(theta) a?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,313
    Thanks
    1291

    Re: Show that v=ωr using dot product or vector products

    v= \omega r doesn't make any sense until you define what those symbols mean! That formula could have many meaning but I suspect it is the relation of the "angular speed" of an object moving in a circle to its "linear speed". If so, yes, "r" has a "physical meaning". It is the radius of the circle. If an object is moving in a circle of radius r, with angular speed, \omega, its linear speed (speed in m/s around the circumference) is v= \omega r. That follows pretty much from the definition of radian measure- the length of a section of a circle of radius r having central angle \theta is \theta r. If r is constant, then the speed with which that length changes is the speed with which \theta changes (which is what "angular speed" means) times the constant radius.

    I have no idea why you would learn "||aXb||=||a||||b||sin(theta)" without learning what aXb meant! That's like learning that the "absolute value of codswallop" is 4 without learning what "coswallop" meant!

    The cross product of two vectors, aXb, is a vector perpendicular both vectors a and b, having length ||a||||b||sin(theta) where ||a|| is the length of vector a and ||b|| is the lengthof vector v.

    You seem to be learning a number of formulas without learning what they mean. That's not a good idea.
    Thanks from happymatthematics
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Dec 2012
    From
    china
    Posts
    30

    Re: Show that v=ωr using dot product or vector products

    Thank you, HallsofIvy.^^
    yes, you're right. Most of the time, I recites things without understanding them.
    do you mind I ask you one more question?
    v = ωR = ωrsin(theta) = ωXr, where R is the radius of the circle
    thus, v=ωXr
    It seems that in ωrsin(theta), ω and r are scalars,
    but in ωXr, ω and r are vectors, why?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 5th 2011, 02:48 AM
  2. Show fnfinite products are equal
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 17th 2010, 11:06 AM
  3. Replies: 2
    Last Post: February 23rd 2009, 10:40 PM
  4. Vector dot products problem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 1st 2008, 11:07 PM
  5. Vector Dot and Cross Products
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 25th 2007, 02:37 PM

Search Tags


/mathhelpforum @mathhelpforum