Question

If the mass of earth is assumed to be m,the radius to be r,the angular velocity be w(wrt centre) and w' wrt sun ,the distance between the centre of earth and sun be l,what will be the earth's kinetic energy?

Answer 1

@Mashy @RnR rotational dynamics :D

Answer 2

shimple :D

Answer 3

add the two kinetic energies.. K.E(rotation) + K.E(revolution)

Answer 4

:O

Answer 5

energies are scalar.. they can be directly added !

Answer 6

how do i calculate them? :(

Answer 7

what will be K.E(rotation) ?

Answer 8

\[\LARGE \frac{1}{2}I \omega ^2\]

Answer 9

^___________________________________^

Answer 10

what is I when you consider earths rotation!?

Answer 11

Mr^2?

Answer 12

DON"T YOU KNOW THE MOMENT OF INERTIA OF A SPHERE ABOUT ITS CENTRE?!??!?!?!!?!?

Answer 13

its a hollow sphere!
so 2/4MR^2

Answer 14

:O.. its a solid sphere .. !!!

Answer 15

oh wth earth is nothollow lol
2/5mr^2 :P

Answer 16

LOL

Answer 17

lol nevermind

Answer 18

wow come to think of it.. totally sidelining

i had thought moment of inertia of a hollow sphere of mass M and radius R would be MR^2 itself.. cause every particle is at the same distance R from the centre.. why is it

2/3 (MR^2) :O

Answer 19

oh no never mind :D i got it!!

Answer 20

:/ great

Answer 21

so anwasy .. now come back

so what is the K.E of rotation!?

Answer 22

\[\LARGE \frac{1}{2} \frac{2}{3}M R^2 \omega\]

Answer 23

correct

now when you calculate the K.E of revolution.. what is the moment of inerita?

Answer 24

2/3 or 2/5? :O

Answer 25

and wait fool.. its not a hollow sphere.. its a SOLID sphere.. sorry.. i dunno M.I values..

Answer 26

we will calculate like this?

ML^2 ?
wahi to?:/ 2/5 hoga

Answer 27

NO.. this time is a point mass (earth).. spinning about sun.. so it ll be just ML^2