Question

The rakius of theearth`s orhit around the sun `1.5 xx 10 ^(11) m`. Calculate the angular velcity and linear velcoityof theearth. Through how much angle does the earth revolve in `2 days`, ?

Answer 1

Here , `r=1.5 xx 10^(11) m, Time period of revolution of earth around the sum is `1 year i.e.
`T=1 year =365 xx 24 xx 60 xx 60 s.`
:. Angular velocity. `omega =(2 pi)/T`
`=(2 xx (22//7)/(365 xx 24 xx 60 xx 60) =1. 99 xx 10^(-1) rad s^(-1)`
Linear velocity, `v=omega r`
`=1.99 x 10^(-7) xx 1.5 xx 10^(11)`
`=2.99 xx 10^(4) ms^(-1)`.
In `365` days, the earth completes one revolution.
Therefore in `36 5) days the earth revolves through an anle `2 pi` radian, In ` 2 days` the earth revloces throught an anle `
`( 2pi) (365) xx (2 xx 22 xx2)/(365) xx 2 (2 xx 22 xx2)/(7xx 365)` =0.034 rad`.