Question

The Radius of the Earth's orbit around the sun 1.5×10^11 m.

Calculate the angular and linear velocity of the earth.

Through how much angle does the earth revolve.

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Answer 1

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Answer 2

Given:

• The radius of the earth = 1.5×$10^{11}$ m

To Find:

• The angular and linear velocity of the earth and how much angle does the earth revolve.

Solution:

We know that earth takes 365 days to complete one revolution around the sun.

∴ Time = 365 days = 365×24×60×60 secs

1. To find the angular velocity.

The formula is given by,

ω = 2π/T → {equation 1}

Where "T" is the time period.

On substituting the values in equation 1 we get,

⇒ ω = (2×3.14)/356×24×60×60 {multiplying the terms}

⇒ ω = 6.28/31536000 {dividing the terms}

⇒ ω = 1.99×$10^{-7}$ rad/sec

2. To find the linear velocity.

The formula is given by,

v = ω r → {equation 2}

Where "ω" is the angular velocity and "r" is the radius.

On substituting the values in equation 1 we get,

⇒ v = 1.99×$10^{-7}$ × 1.5×$10^{11}$ {multiplying the terms}

⇒ v = 2.985×$10^4$ m/s

3. To find the angle of the revolution of the earth.

⇒ (2π/365)×2 = 0.034

∴ The angular velocity = 1.99×$10^{-7}$ rad/sec, the linear velocity = 2.985×$10^4$ m/s and the angle of revolution of the earth = 0.034 rad.