AP Physics C: Mechanics Flashcards: Systems and Center of Mass
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
In the center of mass equation, $\overline{x}_{cm}=\frac{\sum m_{i}\overline{x}_{i}}{\sum m_{i}}$, what does the numerator, $\sum m_{i}\overline{x}_{i}$, represent?
The numerator represents the sum of the products of each object's mass and its position, which is the sum of the moments of the system's parts.
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In the center of mass equation, $\overline{x}_{cm}=\frac{\sum m_{i}\overline{x}_{i}}{\sum m_{i}}$, what does the numerator, $\sum m_{i}\overline{x}_{i}$, represent?
The numerator represents the sum of the products of each object's mass and its position, which is the sum of the moments of the system's parts.
What is the equation to calculate the center of mass for a system of discrete objects along one axis?
The location of a system's center of mass along a given axis can be calculated using the equation $\overline{x}_{cm}=\frac{\sum m_{i}\overline{x}_{i}}{\sum m_{i}}$.
What physical quantity does the denominator, $\int dm$, represent in the center of mass equation for a continuous solid?
The denominator, $\int dm$, represents the integral of all differential mass elements, which is equal to the total mass of the solid.
How can you express a differential mass element, $dm$, using linear mass density, $\lambda$?
By rearranging the definition of linear mass density, a differential mass element can be expressed as $dm = \lambda dl$.
What is the primary difference between finding the center of mass for discrete particles versus a continuous solid?
For discrete particles, we use a summation over individual masses, while for a continuous solid, we must use an integral over differential mass elements.
What is the mathematical expression for linear mass density?
The equation for linear mass density is $\lambda=\frac{d}{dl}m(l)$.
Why is the concept of a system's center of mass useful in physics?
It allows us to describe the motion of a complex system or object as if all its mass were concentrated at a single point, simplifying calculations.
Define a system's center of mass.
A system's center of mass is a specific point whose location is described with respect to the system's constituent parts.
How is the center of mass calculated for a nonuniform solid object?
For a nonuniform solid that can be considered a collection of differential masses, $dm$, the center of mass is calculated using the integral $\overline{r}_{cm}=\frac{\int\overline{r}dm}{\int dm}$.
Define linear mass density ($\lambda$).
The linear mass density of a rod or other linear rigid body is the derivative of the rod's mass with respect to the position of the differential mass element on the rigid body.
What determines the properties of a system?
The properties of a system are determined by the interactions between the objects that are part of the system.