The earth orbits the sun once a year (3.16 multiplied by 10^7 s) in a nearly circular orbit radius 1.50 multiplied by 10^11 m. With respect to the sun, determine the following.
(a) the angular speed of the earth
omega = 2 pi radians / (3.16*10^7 seconds)
then when it asks for the linear speed (part b no doubt), that is omega * r
= [2 pi/3.16*10^7](1.5*10^11] m/s
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To determine the angular speed of the earth, we need to understand the definition of angular speed. Angular speed is the rate at which an object rotates or moves around a central point, measured in radians per second. It represents the angle covered by the object in a given time.
The formula to calculate angular speed is:
Angular Speed = Angle Covered / Time Taken
In this case, the earth's motion around the sun can be considered as a circular motion. The angle covered by the earth in one revolution around the sun is 360 degrees or 2π radians, and the time taken is 1 year or 3.16 x 10^7 seconds.
So, the angular speed (ω) can be calculated as:
ω = 2π / (3.16 x 10^7)
Now, let's calculate the value:
ω ≈ 6.28 / (3.16 x 10^7)
Simplifying further:
ω ≈ 1.99 x 10^(-7) radians/second
Therefore, the angular speed of the earth with respect to the sun is approximately 1.99 x 10^(-7) radians/second.