Systems and Center of Mass - AP Physics C: Mechanics
Card 1 of 30
Identify the center of mass of a uniform rod of length $L$.
Identify the center of mass of a uniform rod of length $L$.
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$\frac{L}{2}$. Symmetry places center at midpoint of uniform rod.
$\frac{L}{2}$. Symmetry places center at midpoint of uniform rod.
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State the condition for the center of mass to lie outside the material of a system.
State the condition for the center of mass to lie outside the material of a system.
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Occurs when the distribution of mass is asymmetric. Unequal mass distribution can place center outside object.
Occurs when the distribution of mass is asymmetric. Unequal mass distribution can place center outside object.
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Which physical property allows the center of mass to simplify analysis of motion?
Which physical property allows the center of mass to simplify analysis of motion?
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Translational motion of a body's center of mass. Center of mass follows Newton's laws for whole system.
Translational motion of a body's center of mass. Center of mass follows Newton's laws for whole system.
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What is the center of mass of a uniform spherical shell?
What is the center of mass of a uniform spherical shell?
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At the geometric center of the sphere. Spherical symmetry places center at geometric center.
At the geometric center of the sphere. Spherical symmetry places center at geometric center.
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What is the relationship between center of mass and stability?
What is the relationship between center of mass and stability?
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Lower center of mass generally increases stability. Lower center reduces tipping tendency.
Lower center of mass generally increases stability. Lower center reduces tipping tendency.
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What is the center of mass for a uniform square plate?
What is the center of mass for a uniform square plate?
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At the geometric center of the square. Square symmetry places center at geometric center.
At the geometric center of the square. Square symmetry places center at geometric center.
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What happens to the center of mass of a system if mass is added symmetrically?
What happens to the center of mass of a system if mass is added symmetrically?
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It remains unchanged. Symmetric addition preserves center position.
It remains unchanged. Symmetric addition preserves center position.
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Which coordinate system is often used to simplify center of mass calculations?
Which coordinate system is often used to simplify center of mass calculations?
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Cartesian coordinate system. Standard coordinate system for position calculations.
Cartesian coordinate system. Standard coordinate system for position calculations.
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What is the center of mass for a uniform rectangular plate of length $L$ and width $W$?
What is the center of mass for a uniform rectangular plate of length $L$ and width $W$?
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At $(\frac{L}{2}, \frac{W}{2})$. Rectangular symmetry places center at geometric center.
At $(\frac{L}{2}, \frac{W}{2})$. Rectangular symmetry places center at geometric center.
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How does rotational motion affect center of mass location?
How does rotational motion affect center of mass location?
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The location of center of mass remains constant. Center of mass position is independent of rotation.
The location of center of mass remains constant. Center of mass position is independent of rotation.
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How does the center of mass of a composite object depend on its parts?
How does the center of mass of a composite object depend on its parts?
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It depends on the distribution of mass and positions of all parts. Center depends on weighted positions of all components.
It depends on the distribution of mass and positions of all parts. Center depends on weighted positions of all components.
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What is the center of mass for a uniform square plate?
What is the center of mass for a uniform square plate?
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At the geometric center of the square. Square symmetry places center at geometric center.
At the geometric center of the square. Square symmetry places center at geometric center.
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What is the center of mass of a system with masses $m_1$ and $m_2$ at the same point?
What is the center of mass of a system with masses $m_1$ and $m_2$ at the same point?
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The center is at the common point of $m_1$ and $m_2$. All mass concentrated at same location.
The center is at the common point of $m_1$ and $m_2$. All mass concentrated at same location.
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Identify the center of mass of a right triangle with base $b$ and height $h$.
Identify the center of mass of a right triangle with base $b$ and height $h$.
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$( \frac{b}{3}, \frac{h}{3} )$. Standard result for right triangle geometry.
$( \frac{b}{3}, \frac{h}{3} )$. Standard result for right triangle geometry.
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How is the center of mass affected by translating a system?
How is the center of mass affected by translating a system?
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The center of mass translates with the system. Translation moves entire system including center of mass.
The center of mass translates with the system. Translation moves entire system including center of mass.
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What is the definition of the center of mass?
What is the definition of the center of mass?
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The point where the total mass of a system is considered to be concentrated. Balance point representing effective mass location.
The point where the total mass of a system is considered to be concentrated. Balance point representing effective mass location.
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Find the center of mass of a uniform disk of radius $R$.
Find the center of mass of a uniform disk of radius $R$.
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At the geometric center of the disk. Circular symmetry places center at disk center.
At the geometric center of the disk. Circular symmetry places center at disk center.
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What is the center of mass of a system of two equal masses at different points?
What is the center of mass of a system of two equal masses at different points?
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Midpoint between the two masses. Equal masses create symmetric center.
Midpoint between the two masses. Equal masses create symmetric center.
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Identify the center of mass of a right circular cone of height $H$.
Identify the center of mass of a right circular cone of height $H$.
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$\frac{H}{4}$ from the base along its axis. Standard result for uniform cone geometry.
$\frac{H}{4}$ from the base along its axis. Standard result for uniform cone geometry.
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What is the effect on the center of mass when an external force is applied?
What is the effect on the center of mass when an external force is applied?
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The center of mass accelerates in the direction of the force. External force causes center of mass acceleration per Newton's second law.
The center of mass accelerates in the direction of the force. External force causes center of mass acceleration per Newton's second law.
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How does the center of mass of a composite object depend on its parts?
How does the center of mass of a composite object depend on its parts?
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It depends on the distribution of mass and positions of all parts. Center depends on weighted positions of all components.
It depends on the distribution of mass and positions of all parts. Center depends on weighted positions of all components.
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What is the center of mass for a uniform rectangular plate of length $L$ and width $W$?
What is the center of mass for a uniform rectangular plate of length $L$ and width $W$?
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At $(\frac{L}{2}, \frac{W}{2})$. Rectangular symmetry places center at geometric center.
At $(\frac{L}{2}, \frac{W}{2})$. Rectangular symmetry places center at geometric center.
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How does rotational motion affect center of mass location?
How does rotational motion affect center of mass location?
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The location of center of mass remains constant. Center of mass position is independent of rotation.
The location of center of mass remains constant. Center of mass position is independent of rotation.
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Identify the effect of a non-uniform mass distribution on the center of mass.
Identify the effect of a non-uniform mass distribution on the center of mass.
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Shifts towards the greater mass concentration. More mass pulls center toward denser regions.
Shifts towards the greater mass concentration. More mass pulls center toward denser regions.
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What role does symmetry play in determining the center of mass?
What role does symmetry play in determining the center of mass?
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Symmetry simplifies finding the center of mass. Symmetric objects have center at geometric center.
Symmetry simplifies finding the center of mass. Symmetric objects have center at geometric center.
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What is the center of mass of a uniform solid sphere?
What is the center of mass of a uniform solid sphere?
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At the geometric center of the sphere. Uniform spheres have center at geometric center.
At the geometric center of the sphere. Uniform spheres have center at geometric center.
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How is the center of mass affected by translating a system?
How is the center of mass affected by translating a system?
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The center of mass translates with the system. Translation moves entire system including center of mass.
The center of mass translates with the system. Translation moves entire system including center of mass.
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State the term for the point where gravitational forces effectively act on a body.
State the term for the point where gravitational forces effectively act on a body.
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Center of gravity. Point where weight effectively acts on object.
Center of gravity. Point where weight effectively acts on object.
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Identify the center of mass of a right triangle with base $b$ and height $h$.
Identify the center of mass of a right triangle with base $b$ and height $h$.
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$( \frac{b}{3}, \frac{h}{3} )$. Standard result for right triangle geometry.
$( \frac{b}{3}, \frac{h}{3} )$. Standard result for right triangle geometry.
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State the condition under which the center of mass coincides with the geometric center.
State the condition under which the center of mass coincides with the geometric center.
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When the mass distribution is uniform. Uniform density makes center coincide with geometry.
When the mass distribution is uniform. Uniform density makes center coincide with geometry.
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