Rotation of a planet, kinetic energy

[Dotty21690]

Homework Statement

Calculate the ratio between the kinetic energy of rotation of a planet (mass=4.30E+24 kg, radius=7.60E+6 m) to the kinetic energy of its center of mass orbiting around its sun at a distance of 1.20E+12 m. Like the Earth, it has a day lasting 24 hours and a year lasting 365.25 days.

Homework Equations

KErot= (1/2)Iw^2 and I believe KE=(1/2)mv^2

The Attempt at a Solution

For the KErot:
KErot= (1/2)((2/5)(4.3E24kg)(7.6E6m)(2pi/(24hr*60min*60sec))^2
and I got 2.62698301E29 J

for the other one:
KE=(1/2)(4.30E24kg)(2pi*1.2E12m/(365.25days*24hrs*60min*60sec))
and got 1.22730571E35 J

I devided KE by KErot and got 467192 for the ratio. but it's wrong and I know I'm doing something wrong but can't figure it out. any help will be great!

 

[tiny-tim]

Welcome to PF!

Hi Dotty21690! Welcome to PF!

(have an omega: ω and a pi: π and try using the X² tag just above the Reply box )

Calculate the ratio between the kinetic energy of rotation of a planet (mass=4.30E+24 kg, radius=7.60E+6 m) to the kinetic energy of its center of mass orbiting around its sun at a distance of 1.20E+12 m. Like the Earth, it has a day lasting 24 hours and a year lasting 365.25 days.
…
For the KErot:
KErot= (1/2)((2/5)(4.3E24kg)(7.6E6m)(2pi/(24hr*60min*60sec))^2
and I got 2.62698301E29 J

for the other one:
KE=(1/2)(4.30E24kg)(2pi*1.2E12m/(365.25days*24hrs*60min*60sec))
and got 1.22730571E35 J

Did you remember to square the radius in both cases?

 

[Dotty21690]

Why would you square the radius in the second part? because isn't the V=Rw?? so the radius wouldn't be squared?

 

[Char. Limit]

It's still mv², which is mR²w².

 

[Dotty21690]

i'm still getting the wrong answer and I don't know why.

 

[Dotty21690]

am I using the wrong equation to find the kinetic energy of the center of mass for the orbit??

 

[tiny-tim]

You should be using 1/2 mv² which is the same as 1/2 m (2πr/T)²

 

[Dotty21690]

so when I plug in my information it will look like this?:

(1/2)(4.3E24kg)((2π*1.2E12m)/31557600sec)^2)

I get 1.22730571E35. but when I do the ratio, I'm getting the answer wrong.

 

[tiny-tim]

Hi Dotty21690!

(please use the X² tag just above the Reply box )

Show us your full calculations (and cancel out the common factors before you start).

 

[Dotty21690]

well I showed the work earlier to get the answers for the KErot and KE, then I divided. I'll post it again though:

For the KErot:
KErot= (1/2)((2/5)(4.3E24kg)(7.6E6m)(2pi/(24hr*60min*60sec))^2
and I got 2.62698301E29 J

for the other one:
KE=(1/2)(4.30E24kg)(2pi*1.2E12m/(365.25days*24hrs*60min*60sec))
and got 1.22730571E35 J

then I divided 1.22730571E35 J/2.62698301E29 J and got 467192.1. I don't even know if I am doing the problem right.

 

[Dotty21690]

turns out the answer was 2.140*10^-6, which I had got at one time, but it said it was wrong :( but I don't know how to get that answer again. so can someone help me with this one?

 

[Char. Limit]

I think you divided your ratio the wrong way. After all, the answer's power is suspiciously close to your answer's power.

 

[Dotty21690]

turns out I did divide the wrong way! but I wonder why I was told the answer was wrong when I did put in 2.140*10^-6, hmm. But thanks guys!