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Q6.1-4PE

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College Physics (Urone)
Found in: Page 221
College Physics (Urone)

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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Short Answer

(a) What is the period of rotation of Earth in seconds?

(b) What is the angular velocity of Earth?

(c) Given that Earth has a radius of 6.4×106 m at its equator, what is the linear velocity at Earth’s surface?

a) The period of rotation of the earth is 86400 s.

b) The angular velocity of the earth is 7.291159×10-5 rad/s.

c) The linear velocity at the earth’s surface is 470  m/s.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Definition of linear velocity

The actual value of the period of rotation of the earth is 23 hours, 56 minutes, and 4 seconds.

This happens because a solar day is longer than a sidereal day. While the earth rotates, it also moves around the sun with an interval of one day.

Step 2: Calculation of the period of the rotation of the earth

The period of rotation of the earth can be calculated as:

=1×24×60×60 s=86400 s

So, the period of the rotation of the earth is 86400 s.

Step 3: Calculation of the angular velocity of the earth

The angular velocity can be calculated as:

=2π86400=7.275×10−5 rad/s

The earth rotates at a moderate angular velocity of 7.275×10−5 rad/s.

Step 4: Calculation of the linear velocity of the earth

Earth’s radius=6.4×106  m.

Thus, the linear speed of any point on the earth’s surface at the equator due to the earth’s rotation is

V=rω=6.4×106×7.3×10−5=470  m/s

Therefore, the linear velocity at the earth’s surface is 470  m/s.

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