Center of Mass of the Human Body

The center of mass (COM) is an important physical concept—it is the point about which objects rotate.

Learning Objective

Estimate the COM of a given object

Key Points

Although a human body has complicated features, the location of the center of mass (COM) could be a good indicator of the body proportions.
We can measure the location of COM with two scales and a wooden beam. The linear and rotational equations of motion gives us the location.
The center of mass of the human body depends on the gender and the position of the limbs. In a standing posture, it is typically about 10 cm lower than the navel, near the top of the hip bones.

Terms

center of mass
The center of mass (COM) is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero.
torque
A rotational or twisting effect of a force; (SI unit newton-meter or Nm; imperial unit foot-pound or ft-lb)

Full Text

The center of mass (COM) is an important physical concept. It is the point on an object at which the weighted relative position of the distributed mass sums to zero—the point about which objects rotate.

Human proportions have been important in art, measurement, and medicine (a well known drawing of the human body is seen in ). Although the human body has complicated features, the location of the center of mass (COM) could be a good indicator of body proportions. The center of mass of the human body depends on the gender and the position of the limbs. In a standing posture, it is typically about 10 cm lower than the navel, near the top of the hip bones. In this Atom, we will learn how to measure the COM of a human body.

Leonardo da Vinci's "The Vitruvian Man"

Vitruvian Man: A drawing created by Leonardo da Vinci. The drawing is based on the correlations of ideal human proportions with geometry described[4] by the ancient Roman architect Vitruvius in Book III of his treatise De Architectura.

First, let's take two scales and a wooden beam (H meter long), long enough to contain the entire body of the subject. Put the scales H meters apart, and place the beam across the scales, as illustrated in . Now, let the subject lie on the beam. Make sure that his/her heels are aligned with one end of the beam. Measure the readings (F₁, F₂) on the scale.

The COM of a Human Body

This figure demonstrates measuring the COM of a human body.

The system (person+beam) has three external forces: gravity on the subject (F_CM), and normal forces from the scales F₁ and F₂. The equation of motion for force (F=ma) will give us:

$F_1 + F_2 = Mg$,

where M is mass of the subject. (We assume that the wooden beam has no mass. ) This equation doesn't provide all the information to locate the COM. However, the equation of motion for torque $( \tau = I\alpha)$ helps.

Since the net torque of the system is zero (hence no rotational acceleration),

$h F_2 - (H-h) F_1 = 0$. (h: COM height)

The COM is chosen as the origin for the torque. Therefore, gravity contributes nothing as a torque. Solving for h and using the equation of motion for force, we get

$h = \frac{HF_1}{Mg}$.

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