Why is it Easier to do Sit-Ups with Hands on Stomach?

[9giddjl]

Hello!

I have a question: Why is it easier to do sit-ups with your hands on your stomach, than with your hands behind your head?

Our teacher told us that it is easier because the moment arm is closer to the axis of rotation.. but I still don't fully understand..because I also read in my physics textbook that, for example, if you were to use a wrench, putting your hands farther away from the axis of rotation makes it easier to rotate the wrench.. and also, what is happening to the force for all of this?

any help would be greatly appreciated :)
thanks in advance ~~

 

[Lok]

When you turn a nut with a wrench, you use an exact amount of energy for it. That Energy can be given by a long distance motion and small force(hand on wrench end) or short distance motion and big force(hand near axis or rotation). The product of the Force and distance is equal in both cases.

 

[xxChrisxx]

What your teacher is talking about is polar moment of inertia http://en.wikipedia.org/wiki/Polar_moment_of_inertia.

It requires less torque to rotate something with a lower polar MOI. The MOI increases linearly with mass but with the square of the distance from the centre point.

This is why it's easy to hold out a tin of beans close to you, but really hard to hold it at arms length. It's the same with the sit up, your CoG will move depending on where you put your arms.

On saying that i'd tend to disagree with your teacher in this specific case, putting your arms at different locations will not tend to alter your centre of gravity much. It's probably that putting your arms behind your head stretchs your back muscles causing them to work against the abs pulling you in.