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Math Help - angular velocity

  1. #1
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    angular velocity

    I cant get the right value out for w. the angular velocity, which is 7.3*10^-5 rad/sec.


    An aircraft travels a straight line from west to east along the equator at a
    constant speed of 100 ms'. Taking the Earth to be a sphere of radius
    6400 km, evaluate the angular velocity.
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  2. #2
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    Quote Originally Posted by lazerx1 View Post
    I cant get the right value out for w. the angular velocity, which is 7.3*10^-5 rad/sec.


    An aircraft travels a straight line from west to east along the equator at a
    constant speed of 100 ms'. Taking the Earth to be a sphere of radius
    6400 km, evaluate the angular velocity.
    are you sure that's the answer? that's not what i got. at least, did they tell you how high the plane was flying?

    the first thing you have to do is "convert" 100m to radians, so instead of m/sec you have rad/sec. so in one second, the plane covers 100m, now recall that s = r \theta, where s is the arclength, r is the radius and \theta is the angle that subtends the arc in radians. since they didn't tell you how high the plane is, you must use r = 6400 km. then we have s = 0.1 km, and so \left( \text{since }\theta = \frac sr \right):

    \frac {0.1 \text{ km}}{\text{sec}} = \frac {\frac {0.1}{6400} \text{ rad}}{\text{sec}} = \frac 1{64000} ~ \frac {\text{rad}}{\text{sec}}
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  3. #3
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    Quote Originally Posted by lazerx1 View Post
    I cant get the right value out for w. the angular velocity, which is 7.3*10^-5 rad/sec.


    An aircraft travels a straight line from west to east along the equator at a
    constant speed of 100 ms'. Taking the Earth to be a sphere of radius
    6400 km, evaluate the angular velocity.
    If 100 m/s is the linear velocity(v), then

    v=r\frac{\theta}{t} where \frac{\theta}{t} is the angular velocity (in radians per unit of time (t)).

    100m/s = 6400000m\left(\frac{\theta}{1s}\right)

    \theta=\frac{100m/s}{6400000m}=1.5625 \times 10^{-5}r/s
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    im quite sure that the answer i quoted is right. v=r X w. Would it have something to do with this cross product. Around the w quoted is a modulus sign.
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lazerx1 View Post
    im quite sure that the answer i quoted is right. v=r X w. Would it have something to do with this cross product. Around the w quoted is a modulus sign.
    well, i dunno. masters and i got the same answer. also, cross-products are only defined for 3-dimensional vectors. what would the vectors be here?
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