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Q.

What is the angular velocity of earth?

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a

\frac{2 π}{86400} rad / \sec

b

\frac{2 π}{3600} rad / \sec

c

\frac{2 π}{24} rad / \sec

d

\frac{2 π}{6400} rad / \sec

answer is A.

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Detailed Solution

Concept: Considering the simple fact that it takes the earth 24 hours to complete one rotation and that its angular frequency can be calculated using the formula frequency = 1/(time required to complete one revolution) , we can use this equation to calculate the earth's angular velocity.
The Earth rotates once every 24 hours.
Earth takes 24 hours to complete one rotation, which is 24 hours = 24×60×60 = 86400 secs
Earth's rotational frequency=

f = \frac{1}{t} = \frac{1}{86400} \sec^{- 1}

Earth’s angular velocity=

ω = 2 πf = \frac{2 π}{86400} rad / \sec

Hence,

\frac{2 π}{86400} rad / \sec

is the angular velocity.
Hence, the correct option is 1.

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