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: 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 2: Identify the variable for total mass in a center of mass calculation.

Answer: $M = \sum m_i$. Sum of all individual masses in the system.

Flashcard 3: 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 4: 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 5: 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 6: 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 7: Identify the variable for total mass in a center of mass calculation.

Answer: $M = \sum m_i$. Sum of all individual masses in the system.

Flashcard 8: 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 9: 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 10: How does the center of mass change if a system is rotated?

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

Flashcard 11: 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: $\frac{0 + 4 + 4}{3} = 2.67$, $\frac{0 + 0 + 4}{3} = 1.33$.

Flashcard 12: What is the formula for the center of mass of a two-particle system?

Answer: $x_{cm} = \frac{m_1x_1 + m_2x_2}{m_1 + m_2}$. Weighted average of positions using mass as weight.

Flashcard 13: 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 14: 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 15: How does the center of mass change if a system is rotated?

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

Flashcard 16: 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 17: 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 18: 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 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: 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 21: 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 22: What is the center of mass for a uniform rod of length $L$?

Answer: $\frac{L}{2}$. For uniform objects, center of mass is at geometric center.

Flashcard 23: 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 24: 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: $\frac{0 + 4 + 4}{3} = 2.67$, $\frac{0 + 0 + 4}{3} = 1.33$.

Flashcard 25: 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 26: 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 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: 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 29: What is the formula for the center of mass of a two-particle system?

Answer: $x_{cm} = \frac{m_1x_1 + m_2x_2}{m_1 + m_2}$. Weighted average of positions using mass as weight.

Flashcard 30: 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 31: 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 32: 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 33: 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 34: Calculate the center of mass for a uniform rod.

Answer: At the midpoint of the rod. Uniform distribution makes center of mass at geometric midpoint.

Flashcard 35: 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 36: 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 37: 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 38: Find the center of mass of a uniform square sheet.

Answer: At the center of the sheet. Square symmetry places center at geometric center.

Flashcard 39: What condition ensures the center of mass is outside the object?

Answer: Non-uniform mass distribution or hollow structure. Examples include rings, hollow objects, or asymmetric shapes.

Flashcard 40: 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 41: 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 42: 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 43: What condition ensures the center of mass is outside the object?

Answer: Non-uniform mass distribution or hollow structure. Examples include rings, hollow objects, or asymmetric shapes.

Flashcard 44: State the formula for the center of mass of a system of particles.

Answer: $\vec{r}_{cm} = \frac{\sum m_i \vec{r}_i}{\sum m_i}$. Vector form for multiple particles using position vectors.

Flashcard 45: Calculate the center of mass for masses 3 kg at (0,0) and 7 kg at (10,0).

Answer: $(x_{cm}, y_{cm}) = (7, 0)$. Weighted average: $\frac{3(0) + 7(10)}{3 + 7} = 7$ for x-coordinate.

Flashcard 46: State the formula for the center of mass of a system of particles.

Answer: $\vec{r}_{cm} = \frac{\sum m_i \vec{r}_i}{\sum m_i}$. Vector form for multiple particles using position vectors.

Flashcard 47: 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 48: 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 49: Find the center of mass of a uniform square sheet.

Answer: At the center of the sheet. Square symmetry places center at geometric center.

Flashcard 50: 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 51: 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 52: 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 53: 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 54: 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 55: 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 56: Calculate the center of mass for masses 3 kg at (0,0) and 7 kg at (10,0).

Answer: $(x_{cm}, y_{cm}) = (7, 0)$. Weighted average: $\frac{3(0) + 7(10)}{3 + 7} = 7$ for x-coordinate.

Flashcard 57: 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 58: 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 59: 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 60: 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 61: 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 62: 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 63: 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 64: Calculate the center of mass for a uniform rod.

Answer: At the midpoint of the rod. Uniform distribution makes center of mass at geometric midpoint.

Flashcard 65: 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 66: 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 67: 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 68: 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 69: 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 70: 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 71: What is the center of mass for a uniform rod of length $L$?

Answer: $\frac{L}{2}$. For uniform objects, center of mass is at geometric center.

Flashcard 72: 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.