angular velocity

**lazerx1** · November 9th 2008, 09:36 AM

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.

**Jhevon** · November 9th 2008, 09:53 AM

Originally Posted by lazerx1

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 $\left( \text{since }\theta = \frac sr \right)$ :

$\frac {0.1 \text{ km}}{\text{sec}} = \frac {\frac {0.1}{6400} \text{ rad}}{\text{sec}} = \frac 1{64000} ~ \frac {\text{rad}}{\text{sec}}$

**masters** · November 9th 2008, 10:08 AM

Originally Posted by lazerx1

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)).

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

$\theta=\frac{100m/s}{6400000m}=1.5625 \times 10^{-5}r/s$

**lazerx1** · November 9th 2008, 10:32 AM

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.

**Jhevon** · November 9th 2008, 10:37 AM

Originally Posted by lazerx1

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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