A physics question in UCM!!?

Question

Calculate the angular speed of rotation of the earth about its axis. If the radius of the earth is 6400km, what is the linear speed of an object situated on the equator?

1.Find angular speed of rotation of earth.

2. what is the linear speed of the object situated on the equator.

Answer the above two questions with complete calculations shown and the formulaes used, Thank u!

Answer 1

>>1.Find angular speed of rotation of earth.<<

Earth rotates once per day. One full rotation is 2π radians. There are 24x60x60 = 86,400 seconds in a day. Thus the angular speed is:

2π/86,400 s = 7.27 x10^-5 rad/s

>>2. what is the linear speed of the object situated on the equator.<<

v = ω · r  = 7.27 x10^-5 rad/s (6400 km) = 0.47 km/s or 465 m/s

Answer 2

The earth spins once on its axis per day. One revolution is 360degrees, or 2*pi radians. Thus,

the angular speed of the earth = 2pi per day

(radians are dimensionless)

convert to units as desired.

to figure out the linear speed of a point on the surface, look up the circumference of the earth (at the equator) (google), since that point has to travel all the way around the outside of the earth, its speed is

1 earth circumference per day.

convert to units as desired.