Understanding Angular Momentum Conservation in Rotating Bodies

[ACLerok]

im supposed to show why angular momentum is conserved in a rotating body with no external torques or forces acting on it. i know to use the I_1*w_1=I_2*w_2 where I is the moment of inertia of the object in motion and w is the angular speed. My qu estiosn are:

which equation for Inertia should I use for a human body sitting on a rotating stool? And how do I calculate angular frequency? Can I just record the amount of rotations per unit of time?

 

[Chi Meson]

Angular frequency is the same as angular velocity: take the number of cycles per second and multiply by 2*pi .

As far as finding the moment of inertia for a body, I'd "chop" a body up into the various parts (torso, thighs, calves, feet,arms, hands, head). Sounds gruesome.

Determine the radial position for center of mass of each part, and approximate mass for each part and add up the various mr^2 for whatever situation you have. It seems rather involved, but check the "center of mass" portion of your textbook; some will have an average human body already chopped up for you. The Giancoli textbook has this.

 

[ACLerok]

OK, thanks alot. when I multiply the no. of cycles per second by 2pi, is that in radians so pi equals 3.14 or in degrees where pi equals 180 degrees?

 

[Chen]

It's just pi - 3.14etc.

 

[ACLerok]

are there anyways to measure the moment of intertia of a person's body with their arms outstreched out and then arms are pulled into their stomach? I was told i didnt need to calculate the intertia of each body part.

 

[cookiemonster]

That's not an easy task no matter how you look at it. People do not make mathematically convenient objects.

cookiemonster

 

[harsh]

are there anyways to measure the moment of intertia of a person's body with their arms outstreched out and then arms are pulled into their stomach? I was told i didnt need to calculate the intertia of each body part.

What you want to do for that is to have a typical rotating stool problem. Have the arms stretched out in one case, and the body is holding two weights of some mass. Then, in the 2nd case, have the weights brought in closer to the body or something like that. I don't think you actually need to show that the moment of inertia of the body to show angular momentum is conserved in the stool problem.

 

[Doc Al]

im supposed to show why angular momentum is conserved in a rotating body with no external torques or forces acting on it. i know to use the I_1*w_1=I_2*w_2 where I is the moment of inertia of the object in motion and w is the angular speed.

Is the problem "show why angular momentum is conserved" or is it "use conservation of angular momentum to explain what happens in the rotating stool example"?

I assume it's the latter question. In which case can't you just use a generic argument like this: When the arms are outstretched there is a rotational inertia I_out. When the arms are pulled in, since the mass is closer to the axis, the new rotational inertia I_in < I_out, so rotational speed must increase in order to conserve angular momentum.

 

[ACLerok]

I am supposed to "use conservation of angular momentum to explain what happens in the rotating stool example" like you stated. I was given a video of a person conducting this experiment. The only info I was given was the distance of the weights to the axis before pulling them in and after pulling them in. Am I able to use I_2*w_2=I_1*w_1 to show it is conserved or should I just explain in words why this has happened?

 

[cookiemonster]

It sounds like you only need a qualitative argument and don't need to bring numbers into this.

cookiemonster

 

[ACLerok]

Ok, Thanks!

 

[ACLerok]

Is there some sort of observation that we can make in order to explain why I2w2=I1w1? I tried thinking of some situations in real life where this relationship can be derived from. Not the concept but the actual mathematical equation.