Question

The earth spins on its axis once a day and orbits the sun once a year (365 1/4 days). Determine the average angular velocity (in rad/s) of the earth as it (a) spins on its axis and (b) orbits the sun. In each case, take the positive direction for the angular displacement to be the direction of the earth's motion.

Answer 1

(a)
`7.27* 10^(- 5)\ rad/s`

(b)
`1.99* 10^(- 7)\ rad/s`

Solution:

As per the question:

The time period of the Earth's spin on its axis, T = 1 day

1 day =
`24* 60* 60 = 86400\ s`

Now,

(a) The Earth's average angular velocity is given by:

`\omega = (2\pi)/(T)`

`\omega = (2\pi)/(86400) = 7.27* 10^(- 5)\ rad/s`

(b) Time period for orbiting the sun, T':

T' =
`365 (1)/(4) = 365.25\ days`

T' =
`365.25* 24* 60* 60 = 3.1557* 10^(7)\ s`

Angular velocity,
`\omega'`:

`\omega' = (2\pi)/(T') = (2\pi)/(3.1557* 10^(7)) = 1.99* 10^(- 7)\ rad/s`