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When the Earth revolves around the sun, the external torque on Earth about the sun is zero, so we can say angular acceleration is zero, then why is angular velocity not constant?

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  • $\begingroup$ Hi Sangeetha. Do you assume the earth to be a perfect sphere? $\endgroup$
    – Kashmiri
    Jun 27, 2021 at 9:00

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It's the angular momentum $I\omega$ that's constant.

As the earth moves closer or further away from the sun its moment of inertia $I$ changes, and so to compensate so can the angular velocity $\omega$, even though there is no torque.

The equation $T=I\alpha$ that you may have been thinking of, is often used in situations where the moment of inertia is constant.

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  • $\begingroup$ Hi, The angular momentum Iw you wrote is about what point? Did you include the spin part? $\endgroup$
    – Kashmiri
    Jun 27, 2021 at 9:03
  • $\begingroup$ No i don't think she included spin of earth in this part, its more likely that she took earth as a point mass of mass m ,that means earths moment of inertia from sun as the axis would be mr^2 ,and as earth us revolving around the sun in elliptical pathway r is not constant ,this shows moment of inertia is not constant. $\endgroup$ Jun 27, 2021 at 11:44
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The angular momentum/angular velocity of the earth is not constant. The oblateness of the earth means that the sun and the planets exert a torque on the earth that tries to turn the axis of rotation to be perpendicular to the plane (the ecliptic) in which the sun and the planets all lie. This torque causes the precession of the equinoxes in which pole direction revolves once every 26,000 years.

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