Question

If the radius of earth is 6400 km what is angular velocity

Answer 1

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The earth has a radius of approximately 6400 km.  How many radians per second is the earth rotating at the equator?

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Expert Answers

CHANGCHENGLIANG | CERTIFIED EDUCATOR

No offense, but to answer the question of how many radians per second the earth is rotating at the equator, the earth's radius of 6400km and also the reference to "equator" need not be given, since rad/s is an angular speed.

Perhaps you have intention to ask "what is the speed of a particular point on Earth at the equator in km/h or m/s?".  I will dwell on this at the last part of this answer.

First of all,

Speed of rotation of earth 1 cycle in 24 hours

= 2 * pi * radian / 24 hrs

= 2 * pi * radian / (24 * 3600 sec)

= 2.3148 * pi * 10^(-5)   rad/sec

= 7.2722 * 10^(-5)  rad/sec

[This works out to about 0.004167 deg/sec or 15 deg/hour]

Now for the speed of a point on the circumference of the Earth at the equator.  Since, by definition, 1 radian will be the angle subtended by an arc which has a length of the radius, the speed of a point on earth on the equator would therefore be given by:

speed (of a point on equator)

= [ 7.2722 * 10^(-8) ] * 6400 km /sec

= 0.4654 km/sec

= 465.4 m/sec .... [ Wow! awesome, isn't it? that's more than 1 round of the stadium in 1 second! And that's faster than the speed of sound which is 333 m/sec]

= 1675.5 km/h .... [ That's more than 10 times the speed of a car at full speed driving on the expressway! ]

 

Answer 2

Explanation:

2π radians / 24 ×3600 sec

2×3.14π\10^-5

7.2722 ×10^-5