1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Circular motion-centripetal acceleration

  1. Apr 26, 2006 #1

    This latex code is giving me some problems. I write one thing, it displays something completely different

    In circular motion velocity only changes direction but not size

    change of velocity - [tex]\Delta v[/tex]
    Change of angle - [tex]\Delta T[/tex]
    Velocity - V
    Centripetal acceleration - a

    delta(V) = V * delta(T)

    When delta(T) approaches its limit (goes to zero), change of velocity has same direction as acceleration vector?

    We compute the magnitude of velocity change with :

    Delta(v) = v * Delta(T)

    I see this being true when change of angle approaches its limit ( goes to zero ), since then length of circular arc ( with radius begin velocity vector ) equals [tex]\Delta v[/tex]. But that is not true if delta(T) is not approaching limit. So how can we use formula

    delta(v) = V * delta(T)

    in cases were delta(T) is not approaching zero, since I assume length of circle arc is quite different than delta(T) if delta(T) doesn't go to zero?

    Last edited: Apr 26, 2006
  2. jcsd
  3. Apr 26, 2006 #2


    User Avatar
    Homework Helper

    I think your original assumption may be incorrect. If you want to relate the linear velocity of the object on the circle circumference with the change in angle, it would be:

    [tex]s = r\theta[/tex]
    [tex]\frac{ds}{dt} = r\frac{d\theta}{dt}[/tex]
    [tex]v = r\frac{d\theta}{dt}[/tex]

    where s is the circle arclength, r is the circle radius, and theta is the angle. The [tex]\frac{d\theta}{dt}[/tex] would be equal to your [tex]\Delta T[/tex].
  4. Apr 27, 2006 #3
    I don't get it. First of all, [tex]v = r\frac{d\theta}{dt}[/tex] is not same formula as delta(v)=v*delta(theta)

    I still don't understand why delta(v) = v * delta(theta) would give us correct result when delta(theta) is anything but [tex]d\theta[/tex] ?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook