AP Physics 1 Flashcards: Systems And Center Of Mass

What this deck covers

This deck focuses on Systems And Center Of Mass, giving you a quick way to review the definitions, rules, and examples that matter most for AP Physics 1.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Find the center of mass of a hollow cylinder.

Answer: At the midpoint of its axis. Cylindrical symmetry puts center at midpoint of central axis.

Flashcard 2: Explain how to find the center of mass of a composite object.

Answer: Divide into simple shapes, find each center, and use weighted average. Standard approach for irregular or complex geometries.

Flashcard 3: Determine the center of mass for a uniform square plate.

Answer: At the intersection of the diagonals. Symmetry makes center of mass coincide with geometric center.

Flashcard 4: What is the center of mass for a symmetric object?

Answer: It is at the geometric center of the object. Symmetry ensures equal mass distribution around center.

Flashcard 5: Find the center of mass of a 3 kg and 5 kg mass placed at (3,0) and (0,4).

Answer: $(x_{cm}, y_{cm}) = (1.875, 2.5)$. Using formula: $x_{cm} = \frac{3(3) + 5(0)}{8} = 1.875$, $y_{cm} = \frac{3(0) + 5(4)}{8} = 2.5$

Flashcard 6: Determine the center of mass for a uniform square plate.

Answer: At the intersection of the diagonals. Symmetry makes center of mass coincide with geometric center.

Flashcard 7: How do external forces affect the center of mass?

Answer: They do not affect its position; only its motion. External forces change motion but not the relative mass distribution.

Flashcard 8: Calculate the center of mass for a 4 kg and 6 kg mass at $(2,2)$ and $(6,6)$.

Answer: $(x_{cm}, y_{cm}) = (4.8, 4.8)$. Using formula: $\frac{4(2) + 6(6)}{10} = 4.8$ for both coordinates.

Flashcard 9: What does the center of mass depend on in a system?

Answer: Mass distribution and positions of the masses. These are the only factors determining center of mass location.

Flashcard 10: Define center of mass.

Answer: The point where the total mass of a system is considered to be concentrated. Useful for analyzing motion as if all mass is at this single point.

Flashcard 11: What is the role of center of mass in collision analysis?

Answer: Simplifies calculations by considering motion at this point. Center of mass motion represents overall system behavior.

Flashcard 12: What is the center of mass for a symmetric solid sphere?

Answer: At the geometric center of the sphere. Spherical symmetry places center at geometric center.

Flashcard 13: What is the effect of internal forces on center of mass?

Answer: Internal forces do not affect the center of mass. Internal forces are between parts of the system.

Flashcard 14: Find the center of mass for masses 2 kg at $(1,0)$ and 8 kg at $(9,0)$.

Answer: $(x_{cm}, y_{cm}) = (7.4, 0)$. Calculation: $\frac{2(1) + 8(9)}{2 + 8} = 7.4$.

Flashcard 15: Explain how to find the center of mass of a composite object.

Answer: Divide into simple shapes, find each center, and use weighted average. Standard approach for irregular or complex geometries.

Flashcard 16: Calculate the $x_{cm}$ for particles at $(2,0)$ and $(8,0)$ with masses 2 kg and 4 kg.

Answer: $x_{cm} = 6$. Calculation: $\frac{2(2) + 4(8)}{2 + 4} = 6$.

Flashcard 17: Find the $x_{cm}$ for equal masses at $(0,0)$ and $(4,0)$.

Answer: $x_{cm} = 2$. Equal masses make center of mass at midpoint: $\frac{0 + 4}{2} = 2$.

Flashcard 18: What happens to the center of mass if a mass moves within a system?

Answer: The center of mass shifts according to the mass movement. Center of mass follows the moving mass proportionally.

Flashcard 19: Identify the formula for the $y$-coordinate of the center of mass.

Answer: $y_{cm} = \frac{\sum m_i y_i}{\sum m_i}$. Same formula as x-coordinate but using y-positions.

Flashcard 20: How does the center of mass change if a system is rotated?

Answer: It remains unchanged. Rotation doesn't change relative mass positions.

Flashcard 21: Identify the center of mass for a triangle.

Answer: At the centroid, intersection of medians. For triangles, centroid and center of mass coincide when uniform.

Flashcard 22: What is the center of mass formula for continuous mass distribution?

Answer: $\vec{r}_{cm} = \frac{1}{M}\int \vec{r} \ dm$. Integral form for objects with continuous mass distribution.

Flashcard 23: What happens to the center of mass in uniform acceleration?

Answer: It accelerates uniformly. Center of mass follows Newton's second law like a point mass.

Flashcard 24: What is the center of mass of a uniform circular disk?

Answer: At the center of the disk. Circular symmetry places center of mass at geometric center.

Flashcard 25: What is the significance of the center of mass in motion analysis?

Answer: It simplifies the analysis by treating motion as if all mass is at this point. Allows treating complex systems as point masses.

Flashcard 26: Identify the formula for the $z$-coordinate of the center of mass.

Answer: $z_{cm} = \frac{\sum m_i z_i}{\sum m_i}$. Extension to three-dimensional systems using z-coordinates.

Flashcard 27: Determine the center of mass of a thin rectangular plate.

Answer: At the intersection of the diagonals. Rectangular symmetry puts center at intersection of diagonals.

Flashcard 28: How is the center of mass related to rotational motion?

Answer: It is the axis about which the object rotates. Objects tend to rotate about their center of mass.

Flashcard 29: What is the effect of friction on the center of mass location?

Answer: Friction does not affect the location of the center of mass. Friction is an external force affecting motion, not position.

Flashcard 30: Calculate the center of mass for equal masses at $(0,0)$, $(4,0)$, $(4,4)$.

Answer: $(x_{cm}, y_{cm}) = (2.67, 1.33)$. Three equal masses: $\frac{0 + 4 + 4}{3} = 2.67$, $\frac{0 + 0 + 4}{3} = 1.33$.