Hello, I'm trying to bone up on my conservation of angular momentum skills as well as my ice skating skills so I can be like my hero, Michio Kaku.
Unfortunately my ice skating skills are better than my physics skills, so I thought y'all might be able to help. Here's the question, if angular momentum, L, equals the moment of inertia of a body, I, multiplied by its angular velocity, ω, then does [itex]L=mr^2(2πf)[/itex]?
Now, if that's true, then does [itex]r=\sqrt{L/m2πf}[/itex]?
And, accordingly, [itex]f=L/m2πr^2[/itex]?
I just attempted to derive these myself so I don't know if I'm missing something here.
Plugging in some values, then, if I weighed 100 kg and started spinning at 1 cycle per second with my arms extended at a 1 meter radius, then would my angular momentum be 628.32 joule-seconds?
Now say we were to conserve this figure as I varied my "moment" during my spin by moving my arms inward and outward of my torso. Say I brought my arms in so that my radius was .5 meters instead of 1 meter. Would my rotation rate then be 4 cycles per second?
Finally, if I decided I wanted to rotate at a comfortable 2 cycles per second, would I need to move my arms to a position whereby my radius was 0.7 meters?
Am I calculating these figures correctly? Thanks for your help. Also, I do have one follow up question once I get all of this checked out.
Unfortunately my ice skating skills are better than my physics skills, so I thought y'all might be able to help. Here's the question, if angular momentum, L, equals the moment of inertia of a body, I, multiplied by its angular velocity, ω, then does [itex]L=mr^2(2πf)[/itex]?
Now, if that's true, then does [itex]r=\sqrt{L/m2πf}[/itex]?
And, accordingly, [itex]f=L/m2πr^2[/itex]?
I just attempted to derive these myself so I don't know if I'm missing something here.
Plugging in some values, then, if I weighed 100 kg and started spinning at 1 cycle per second with my arms extended at a 1 meter radius, then would my angular momentum be 628.32 joule-seconds?
Now say we were to conserve this figure as I varied my "moment" during my spin by moving my arms inward and outward of my torso. Say I brought my arms in so that my radius was .5 meters instead of 1 meter. Would my rotation rate then be 4 cycles per second?
Finally, if I decided I wanted to rotate at a comfortable 2 cycles per second, would I need to move my arms to a position whereby my radius was 0.7 meters?
Am I calculating these figures correctly? Thanks for your help. Also, I do have one follow up question once I get all of this checked out.
