Jeslek
Banned
I'm getting muddled with the units... Here is the question.
Define the moment of inertia of a planet I. The spin energy of a planet that rotates with angular velocity w is Iw²/2. For the Earth, this changes because the spin changes at a rate of approximately 2 msec/century. Calculate the loss of energy of the Earth due to its spindown.
You can take I = Mr²/3 where M = 6.0 x 10^24 kg, and r = 6.37 x 10^6 m.
Express your answer in watts.
Now lets see. Watts is defined as kg·m²/sec³. Joule is defined as kg·m²/sec² since watts is also J/sec.
I = Mr²/3 = <some number> kg·m².
Now I'm stuck. How do I express angular velocity? And the change in w is 2 msec/century. Now we have to convert it to standard units, so then you end up with <some number> sec/sec. This unit is essentially dimensionless.
H E L P.
Define the moment of inertia of a planet I. The spin energy of a planet that rotates with angular velocity w is Iw²/2. For the Earth, this changes because the spin changes at a rate of approximately 2 msec/century. Calculate the loss of energy of the Earth due to its spindown.
You can take I = Mr²/3 where M = 6.0 x 10^24 kg, and r = 6.37 x 10^6 m.
Express your answer in watts.
Now lets see. Watts is defined as kg·m²/sec³. Joule is defined as kg·m²/sec² since watts is also J/sec.
I = Mr²/3 = <some number> kg·m².
Now I'm stuck. How do I express angular velocity? And the change in w is 2 msec/century. Now we have to convert it to standard units, so then you end up with <some number> sec/sec. This unit is essentially dimensionless.
H E L P.
