Question

Why is it more difficult to do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer this.

Short answer

It is more difficult to do a sit-up with your hands behind your head because of the greater torque required in this case.

Step-by-step solution

Understanding the variation of rotational inertia in different positions of the body

Consider case (1) when the arms are behind the head.In this case, the value of rotational inertia decreases when the person tries to sit up. The body center of mass shifted to a new position.

Consider case (2) when the arms are extended in the front.In this case, the value of rotational inertia increases when the person tries to sit up.

Understanding the effect on torque while in the sit-up position

A person needs torque that will enable him to rotate his upper body. Torque is required to rotate the body from the sitting down position to the sitting up position. When the value of rotational inertia increases, the value of torque also increases.

The diagram of a person trying to sit up from lying down can be shown as follows:

Here, the person requires extra force in sitting up from the laying down position.

Understanding case (1) when the arms are behind the head 

The diagram of the person sitting up with the arms behind his head can be shown as:

Consider a person who tries to sit up with the hands behind his head as the body center of mass moves away from the axis of rotation and shifts to the back. Here, a greater rotational inertia is required to sit up when the hands are behind the head. The body inertia decreases with a small amount.

So, it would be more difficult to sit up as it would require an extra amount of energy.

Understanding case (2) when the arms are extended in the front

The diagram of the person sitting up with the arms extended in the front can be shown as follows:

Consider a person who tries to sit up with his hands extended in from of him. The body’s moment of inertia decreases more. Here, the lower rotational inertia must applied in the sit up when the hands are extended in the front.

So, a lower torque is required in this case.

Thus, from the above two cases, it can be concluded that it is more difficult to do a sit-up with hands behind heads because of the greater torque required in this case.