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Math Help - angular displacement

  1. #1
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    angular displacement

    After 10.0 s, a spinning roulette wheel at a casino has slowed down to an angular velocity of +1.82 rad/s.

    During this time, the wheel has an angular acceleration of -4.25 rad/s2.

    Determine the angular displacement of the wheel.
    in rad

    ...

    so is 1.82 rad/s the w0 or the wf?

    and i'm trying to find theta i believe.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    After 10.0 s, a spinning roulette wheel at a casino has slowed down to an angular velocity of +1.82 rad/s.

    During this time, the wheel has an angular acceleration of -4.25 rad/s2.

    Determine the angular displacement of the wheel.
    in rad

    ...

    so is 1.82 rad/s the w0 or the wf?

    and i'm trying to find theta i believe.
    \frac{d^2}{dt^2}\theta = -4.24

    so:

    \frac{d}{dt}\theta = -4.24t + \theta'_0

     <br />
\theta=\frac{-4.24 t^2}{2}+\theta'_0 t + \theta_0<br />

    We may assume that \theta_0=0 so we have:

     <br />
\theta=\frac{-4.24 t^2}{2}+\theta'_0 t<br />

    Now put in your values and if needed reduce the result modulo 2\pi.

    Note you are give \theta_{t=10}=1.82 rather than the value of \theta_{0}, so you will have to work that out.

    RonL
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  3. #3
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    what is theta' ?
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  4. #4
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    Quote Originally Posted by rcmango View Post
    what is theta' ?
    \theta' is angular velocity

    RonL
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    i think you gave me an infraction point because you mis understood my question, which is


    what is theta ' what is the purpose in other words.

    the theta with the '

    not the answer!

    there are two thetas?

    okay i got it 231 rad

    thankyou.
    Last edited by rcmango; November 24th 2007 at 02:04 AM.
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  6. #6
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    Quote Originally Posted by rcmango View Post
    i think you gave me an infraction point because you mis understood my question, which is


    what is theta ' what is the purpose in other words.

    the theta with the '

    not the answer!

    there are two thetas?

    okay i got it 231 rad

    thankyou.
    I don't know if you are in a Calculus class? \theta ^{\prime} is the time derivative of \theta. You would call it the angular velocity.

    -Dan
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by rcmango View Post
    After 10.0 s, a spinning roulette wheel at a casino has slowed down to an angular velocity of +1.82 rad/s.

    During this time, the wheel has an angular acceleration of -4.25 rad/s2.

    Determine the angular displacement of the wheel.
    in rad

    ...

    so is 1.82 rad/s the w0 or the wf?

    and i'm trying to find theta i believe.
    As always, start with a coordinate system. I'm going to set an origin for \theta to be at the point where the 10 s time interval started. (There is a direction for the angular displacement, but I'm going to assume that you haven't seen this yet and skip it.)

    Here's what we know:
    t = 10~s
    \theta _0 = 0~rad~~~~\theta = ?
    \omega_0 = ? ~~~~\omega = 1.82~rad/s
    \alpha = -4.25~rad/s

    We want \theta. Typically I simply apply one of my four "master" equations to solve this kind of problem, but all of them depend on a value of \omega _0:
    \theta = \theta _0 + \omega _0t + \frac{1}{2} \alpha t^2

    \theta = \theta _0 + \frac{1}{2}( \omega _0 + \omega )t

    \omega = \omega _0 + \alpha t

    \omega ^2 = \omega _0^2 + 2 \alpha ( \theta - \theta _0 )

    (Since this kind of situation doesn't happen very often I don't keep an equation for it in my back pocket, as it were.)

    So we need to use an equation to find \omega _0, then use another to find \theta.

    Well:
    \omega = \omega _0 + \alpha t

    \omega_0 = \omega  - \alpha t = 1.82 - (-4.25)(10) = 44.32~rad/s

    And thus
    \theta = \theta _0 + \omega _0t + \frac{1}{2} \alpha t^2

    \theta = (44.32)(10) + \frac{1}{2} (-4.25) (10)^2 = 230.7~rad

    -Dan
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  8. #8
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    thankyou, ya i recognized the derivative, i just wasn't sure which theta to solve for the actual angular velocity.
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  9. #9
    Grand Panjandrum
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    Quote Originally Posted by rcmango View Post
    i think you gave me an infraction point because you mis understood my question, which is


    what is theta ' what is the purpose in other words.

    the theta with the '

    not the answer!

    there are two thetas?

    okay i got it 231 rad

    thankyou.
    No I gave you an infraction because you posted this question twice in different sub-fora, which is not permitted.

    RonL
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