Question

The earth revolves around the sun in an orbit of 1.5 × 10^11m per radian once in year. (a) calculate angular velocity . (b) Linear velocity of the earth.​

Answer 1

GIVEN :

• The earth revolves around the sun in an orbit of $\sf 1.5 \times 10^{11}$ per radian once in a year.

TO FIND :

• Angular velocity = ?
• Linear velocity of the earth = ?

SOLUTION :

First, to find the angular velocity = ?

Give that Time, t = 1 year.

$\implies \sf 365 \times 24 \times 60 \times 60$

$\implies \sf Angular \ velocity, \ \omega \ = \ \dfrac {2 \pi}{l}$

$\implies \sf \dfrac {2 \times \dfrac {22}{7}}{365 \times 24 \times 60 \times 60}$

$\implies \sf 1.99 \times 10^{-7} \times 1.5 \times 10^{11}$

$\implies \sf 2.99 \times 10^4 \ m/s$

Now,

$\implies \sf \dfrac {2 \pi}{365} \times 2$

$\implies \sf \dfrac {2 \times 22 \times 2}{7 \times 365}$

$\implies \sf 0.034 \ radian.$