Angular Momentum and Angular kinetic energy about the center of the sun.

[Wasseem92]

Homework Statement

The Earth is approximately 1.5x10^8 km from the sun. what is the Earth's angular momentum about the center of the sun. Note the mass of the Earth is 5.97x10^24.

Homework Equations

The Attempt at a Solution

I got the answer, but my question is, when finding the velocity: which is 2pir/time the Earth takes to revolve, do we use 2pi/time or 2pir/time. i have this question because my teacher in some examples uses r and in some doesnt. Can someone help me with when and why we use the radius?

 

[da_nang]

It's to differentiate between angular and tangential velocity.

Angular velocity: dθ/dt
Tangential velocity: ds/dt = r*dθ/dt, since s = θ*r.

So, when it says 2π/time, it's angular velocity, and when it says 2πr/time it's tangential velocity. For example, say you have a ball rolling on very slippery ice. It's kinetic energy isn't just ½mv² but also ½Iω², since it's also rotating. These velocities can be converted into one another due to the relation v = ωr.