Earth Rotation?

Question

It takes 23 hours 56 minutes and 4 seconds for the earth to make one revolution (mean sidereal day). What is the angular speed of the earth?

Assume the earth is spherical. Relative to someone on the rotation axis, what is the linear speed of an object on the surface if the radius vector from the center of the earth to the object makes an angle of 51.0° with the axis of rotation. The radius of the earth is 6.37×103 km.

What is the acceleration of the object on the surface of the earth in the previous problem?

Answer 1

The angular velocity of the earth is 360 degrees per aprox 24 hrs. So its equal to 15 degrees per hour =w
the linear velocity ^2 is = w x r;where r is radius of earth
At 51 degree latitude the linear velocity ^2 would be equal to =w x rcos51degree
Acceleration at the surface of the earth is=radius of the earh divided by the time ^2 at the surface of the earth is aprox =9.80 meter/sec^2

Answer 2

Angular speed = 360 degrees in 23h 56m 4s

Equatorial Distance (ED) from axis = Earth radius * sin(51 degrees)

Local circumference (LD) = ED * 2pi
Linear speed = LC / (23h 56m 4s)

Local acceleration: exercise for the student

Answer 3

Find area by A= pie 2r or A= 3.14*(6.37e^3km)*2 this gives you the circumference then take v=m/s or v=A/s -> v= (3.14*(6.37e^3km)*2)/ 23 hours 56 minutes and 4 seconds. you must convert hours and minutes to seconds to speed per second unless it asks for minutes or hours.