# Explain how the question "What is the linear velocity of a point on the equator?" requires an...

## Question:

Explain how the question "What is the linear velocity of a point on the equator?" requires an assumption about the reference frame used. Show how the answer changes as you change reference frames.

## Reference Frame:

The velocity of an object in a reference frame is the velocity of another reference frame plus the velocity of the object to the later frame.

{eq}\vec v_o = \vec v_f + \vec v_{fo} {/eq}

The earth's equator is about 40075 m. The period of the earth rotation is about 23.93 hours.

The orbit speed of the earth is about 30 km/s.

## Answer and Explanation:

When we ask the question "What is the linear velocity of a point on the equator?", we usually assumes the reference frame is on the rotation axis of the earth. The point on the equator is traveling in a uniform circular motion. The linear speed is equal to the circumference, the equator, divide by the time for one revolution, which is about

{eq}v = \dfrac dt = \dfrac{40075}{23.93*60*60} = \boxed{\bf 465 \ \rm m/s} {/eq}

If we change the reference frame to the sun, the answer will be not the same. The speed of the point on the equator would be

{eq}\vec v = \vec v_f + \vec v_{fo} {/eq}

The earth's orbit speed is about 30 km/s, much larger than 465 m/s. The resultant speed will be between 29535 m/s and 30465 m/s.

#### Learn more about this topic:

Inertial Frame of Reference: Definition & Example

from General Studies Science: Help & Review

Chapter 4 / Lesson 12
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