No you guys, most shapes do not have a center of mass with this property (but some do)

The video explores the misconception that any plane through the center of mass of a 3D object cuts it in half. While this is true for objects with obvious symmetry like circles and squares, it does not hold for equilateral triangles or tetrahedrons. The video provides a mathematical analysis and proof using an equilateral triangle to demonstrate that no such point exists where any line through it will bisect the triangle. The conclusion extends this finding to other shapes, emphasizing that not all objects have a magical point for bisecting planes.

What is the common misconception about the center of mass in 3D objects?

• It is the point where the object is heaviest.

• It is the point where the object is lightest.

• Any plane through it cuts the object in half.

• It is always located at the geometric center.

Which of the following shapes has a center of mass where any line through it cuts the shape in half?

• Equilateral triangle

• Rectangle

• Circle

• Pentagon

Why does the property of a center of mass cutting an object in half not hold for an equilateral triangle?

• The triangle has unequal side lengths.

• The centroid does not divide the triangle into equal areas.

• The triangle is not symmetrical.

• The centroid is not equidistant from all sides.

What is the length of the height below the purple line in the equilateral triangle example?

• 1

• 2 Root 3 / 3

• Root 3 / 3

• Root 3

Which other 3D shape was mentioned as not having the property where any plane through the center of mass cuts it in half?

• Cube

• Sphere

• Tetrahedron

• Cylinder