What is the angle of rotation?The earth has a radius of approximately 6400 km. If a point on the circumferathe moves by 2 kilometers what is the angle of rotation about the origin?
Your question is a little difficult to understand. I assume by origin you mean the center about which it is rotating. Now you want to know how many kilometers it has rotated at the origin. Rotation is measured in terms of an angle and kilometer is a unit of displacement. It is not possible to define anything like the number of kilometers it has rotated at the origin.
Now if you want to know that if a point on the circumference which is a circle of radius 6400 km moves by 2 km, what the angle of rotation is, it can be calculated as follows. For a 360 degree rotation about the origin, the point moves by 2*pi*6400 kilometers. For a movement of 2 kilometers the angle of rotation about the origin is equal to 360*2/ 2*pi*6400 = 0.0179 degree.
[ I have made the appropriate changes in the question]
The radius of the earth is 6400 kms. If the point is on the surface of the earth moves by 2 kilometer due to rotation, then it is as good as the point describes an arc of circle whose centre is at the centre of earth and the radius is the radius of the earth.
The relation between the arc and the angle the arc subtends at the centre of the cicrle is given by:
Arc length = angle in radians* radius of the circle.
We substitute in the above relation , arc length = 2km. Radius = 6400 km.
2km = angle/6400km
Angle subtended at the centre of earth= 2/6400 = 0.0003125 radians.
1 radian = 180/pi = 57.29577951 degree.
Or angle subtended at the centre of earth = 0.0003125*5729577951 = 0.01704931degrees. = 1minute, 4.457752 seconds .