Center of mass

Center of mass for several objectsThe center of mass is the average position of all the mass contained in an object (see page 268). That means that there is an equal quantity of mass on either side of any plane splitting an object through the center of mass regardless of which plane is chosen. The center of mass is sometimes called the “center of gravity” because it represents the average point at which the force of gravity acts on an object. Read the text aloud
When an object is rotating and translating at the same time we often separate the motions into two parts using the center of mass as a reference.
  1. The linear motion is the translation of the center of mass. The linear momentum is the object’s mass times the velocity of the center of mass.
  2. The rotational motion is about the center of mass. The angular momentum is defined relative to an axis passing through the center of mass.
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Center of mass of a hula hoop is located at its center, which is outside its bodyFor geometrical objects, such as a solid sphere or cube, the center of mass is located at the object’s geometrical center. While some irregularly shaped objects may still have their center of mass located inside them, others can have the center of mass outside their body. Where is the center of mass of a hula hoop located? The answer is at its center, even though no mass is located there! Read the text aloud
The beautiful feature of the center of mass is that it allows us to simplify a complex situation. The force of gravity can be assumed to act on the center of mass, as if all the mass of the object were concentrated at that point. Read the text aloud Show Point masses and gravity
Stability and the center of mass:  which truck will tip over?The center of mass represents the balance point: If you placed the object on a pencil tip located directly below the center of mass, the forces should balance! Imagine a truck driving horizontally along a steep slope. Will it tip over? The force of gravity acts on the center of mass of the truck; gravity creates a torque about the truck’s wheelbase. If the truck’s center of mass is located vertically above or inside the wheelbase, the torque will act to keep the truck upright. But if the truck’s center of mass is located beyond the wheelbase, the torque exerted by gravity will cause it to tip over. This is why the heaviest cargo should be loaded near the bottom of the truck! Read the text aloud
Will this stack of books fall off the edge of the table?A student stacked 10 textbooks along the edge of a desk, as shown in the figure at left. If all the textbooks are identical and have uniform density, will the stack fall off the edge of the desk? Show

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