Understanding and Finding Center of Mass - AP Physics C: Electricity and Magnetism
Card 1 of 44
Doing which of the following would allow you to find the center of mass of an object?
Doing which of the following would allow you to find the center of mass of an object?
Tap to reveal answer
Center of mass can be found by spinning an object. It will naturally spin around its center of mass, due to the concept of even distribution of mass in relation to the center of mass. Shape and mass are important factors in this property, but the most improtant factor is the mass distribution.
Center of mass can be found by spinning an object. It will naturally spin around its center of mass, due to the concept of even distribution of mass in relation to the center of mass. Shape and mass are important factors in this property, but the most improtant factor is the mass distribution.
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If two masses, 
and 
are placed on a seesaw of length 
, where must the fulcrum be placed such that the seesaw remains level?
If two masses,
Tap to reveal answer
This question asks us to find the center of mass for this system. We know that the center of mass resides a distance 
from the first mass such that:
In this case:
Plug in known values and solve.
This question asks us to find the center of mass for this system. We know that the center of mass resides a distance
In this case:
Plug in known values and solve.
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If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?
If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?
Tap to reveal answer
Changing the position of the fulcrum by moving it to the left means the center of mass will be to the right of the new position. Therefore, the scale will tip right. Adding more mass to the left end will rebalance the scale. None of the other options make sense. Adding more mass to the new fulcrum position will not change the balance of the scale because that mass is a negligible distance from the new fulcrum position and does nothing to change the masses on either side.
Changing the position of the fulcrum by moving it to the left means the center of mass will be to the right of the new position. Therefore, the scale will tip right. Adding more mass to the left end will rebalance the scale. None of the other options make sense. Adding more mass to the new fulcrum position will not change the balance of the scale because that mass is a negligible distance from the new fulcrum position and does nothing to change the masses on either side.
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Three 
point masses are at the points 
, 
and
and a 
point mass is at the point 
.
How far from the origin is the center of mass of the system?
Three
How far from the origin is the center of mass of the system?
Tap to reveal answer
To find the center of mass, we have to take the weighted average of the x coordinates and the y coordinates.
Measures: 
Measures
First, we take the weighted measurement of the x-axis:
We can see that the result of the x-axis contribution is equal to 
.
Now, let's look at the y-axis contribution:
This equals to 
Now that we have the x and y components, we take the root of squares to get the final answer:
This will give us 
To find the center of mass, we have to take the weighted average of the x coordinates and the y coordinates.
First, we take the weighted measurement of the x-axis:
We can see that the result of the x-axis contribution is equal to
Now, let's look at the y-axis contribution:
This equals to
Now that we have the x and y components, we take the root of squares to get the final answer:
This will give us
← Didn't Know|Knew It →
Doing which of the following would allow you to find the center of mass of an object?
Doing which of the following would allow you to find the center of mass of an object?
Tap to reveal answer
Center of mass can be found by spinning an object. It will naturally spin around its center of mass, due to the concept of even distribution of mass in relation to the center of mass. Shape and mass are important factors in this property, but the most improtant factor is the mass distribution.
Center of mass can be found by spinning an object. It will naturally spin around its center of mass, due to the concept of even distribution of mass in relation to the center of mass. Shape and mass are important factors in this property, but the most improtant factor is the mass distribution.
← Didn't Know|Knew It →
If two masses, and are placed on a seesaw of length , where must the fulcrum be placed such that the seesaw remains level?
If two masses,
Tap to reveal answer
This question asks us to find the center of mass for this system. We know that the center of mass resides a distance from the first mass such that:
In this case:
Plug in known values and solve.
This question asks us to find the center of mass for this system. We know that the center of mass resides a distance
In this case:
Plug in known values and solve.
← Didn't Know|Knew It →
If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?
If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?
Tap to reveal answer
Changing the position of the fulcrum by moving it to the left means the center of mass will be to the right of the new position. Therefore, the scale will tip right. Adding more mass to the left end will rebalance the scale. None of the other options make sense. Adding more mass to the new fulcrum position will not change the balance of the scale because that mass is a negligible distance from the new fulcrum position and does nothing to change the masses on either side.
Changing the position of the fulcrum by moving it to the left means the center of mass will be to the right of the new position. Therefore, the scale will tip right. Adding more mass to the left end will rebalance the scale. None of the other options make sense. Adding more mass to the new fulcrum position will not change the balance of the scale because that mass is a negligible distance from the new fulcrum position and does nothing to change the masses on either side.
← Didn't Know|Knew It →
Three point masses are at the points , and
and a point mass is at the point .
How far from the origin is the center of mass of the system?
Three
How far from the origin is the center of mass of the system?
Tap to reveal answer
To find the center of mass, we have to take the weighted average of the x coordinates and the y coordinates.
Measures: Measures
First, we take the weighted measurement of the x-axis:
We can see that the result of the x-axis contribution is equal to .
Now, let's look at the y-axis contribution:
This equals to
Now that we have the x and y components, we take the root of squares to get the final answer:
This will give us
To find the center of mass, we have to take the weighted average of the x coordinates and the y coordinates.
First, we take the weighted measurement of the x-axis:
We can see that the result of the x-axis contribution is equal to
Now, let's look at the y-axis contribution:
This equals to
Now that we have the x and y components, we take the root of squares to get the final answer:
This will give us
← Didn't Know|Knew It →
Doing which of the following would allow you to find the center of mass of an object?
Doing which of the following would allow you to find the center of mass of an object?
Tap to reveal answer
Center of mass can be found by spinning an object. It will naturally spin around its center of mass, due to the concept of even distribution of mass in relation to the center of mass. Shape and mass are important factors in this property, but the most improtant factor is the mass distribution.
Center of mass can be found by spinning an object. It will naturally spin around its center of mass, due to the concept of even distribution of mass in relation to the center of mass. Shape and mass are important factors in this property, but the most improtant factor is the mass distribution.
← Didn't Know|Knew It →
If two masses, and are placed on a seesaw of length , where must the fulcrum be placed such that the seesaw remains level?
If two masses,
Tap to reveal answer
This question asks us to find the center of mass for this system. We know that the center of mass resides a distance from the first mass such that:
In this case:
Plug in known values and solve.
This question asks us to find the center of mass for this system. We know that the center of mass resides a distance
In this case:
Plug in known values and solve.
← Didn't Know|Knew It →
If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?
If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?
Tap to reveal answer
Changing the position of the fulcrum by moving it to the left means the center of mass will be to the right of the new position. Therefore, the scale will tip right. Adding more mass to the left end will rebalance the scale. None of the other options make sense. Adding more mass to the new fulcrum position will not change the balance of the scale because that mass is a negligible distance from the new fulcrum position and does nothing to change the masses on either side.
Changing the position of the fulcrum by moving it to the left means the center of mass will be to the right of the new position. Therefore, the scale will tip right. Adding more mass to the left end will rebalance the scale. None of the other options make sense. Adding more mass to the new fulcrum position will not change the balance of the scale because that mass is a negligible distance from the new fulcrum position and does nothing to change the masses on either side.
← Didn't Know|Knew It →
Three point masses are at the points , and
and a point mass is at the point .
How far from the origin is the center of mass of the system?
Three
How far from the origin is the center of mass of the system?
Tap to reveal answer
To find the center of mass, we have to take the weighted average of the x coordinates and the y coordinates.
Measures: Measures
First, we take the weighted measurement of the x-axis:
We can see that the result of the x-axis contribution is equal to .
Now, let's look at the y-axis contribution:
This equals to
Now that we have the x and y components, we take the root of squares to get the final answer:
This will give us
To find the center of mass, we have to take the weighted average of the x coordinates and the y coordinates.
First, we take the weighted measurement of the x-axis:
We can see that the result of the x-axis contribution is equal to
Now, let's look at the y-axis contribution:
This equals to
Now that we have the x and y components, we take the root of squares to get the final answer:
This will give us
← Didn't Know|Knew It →
Doing which of the following would allow you to find the center of mass of an object?
Doing which of the following would allow you to find the center of mass of an object?
Tap to reveal answer
Center of mass can be found by spinning an object. It will naturally spin around its center of mass, due to the concept of even distribution of mass in relation to the center of mass. Shape and mass are important factors in this property, but the most improtant factor is the mass distribution.
Center of mass can be found by spinning an object. It will naturally spin around its center of mass, due to the concept of even distribution of mass in relation to the center of mass. Shape and mass are important factors in this property, but the most improtant factor is the mass distribution.
← Didn't Know|Knew It →
If two masses, and are placed on a seesaw of length , where must the fulcrum be placed such that the seesaw remains level?
If two masses,
Tap to reveal answer
This question asks us to find the center of mass for this system. We know that the center of mass resides a distance from the first mass such that:
In this case:
Plug in known values and solve.
This question asks us to find the center of mass for this system. We know that the center of mass resides a distance
In this case:
Plug in known values and solve.
← Didn't Know|Knew It →
If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?
If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?
Tap to reveal answer
Changing the position of the fulcrum by moving it to the left means the center of mass will be to the right of the new position. Therefore, the scale will tip right. Adding more mass to the left end will rebalance the scale. None of the other options make sense. Adding more mass to the new fulcrum position will not change the balance of the scale because that mass is a negligible distance from the new fulcrum position and does nothing to change the masses on either side.
Changing the position of the fulcrum by moving it to the left means the center of mass will be to the right of the new position. Therefore, the scale will tip right. Adding more mass to the left end will rebalance the scale. None of the other options make sense. Adding more mass to the new fulcrum position will not change the balance of the scale because that mass is a negligible distance from the new fulcrum position and does nothing to change the masses on either side.
← Didn't Know|Knew It →
Three point masses are at the points , and
and a point mass is at the point .
How far from the origin is the center of mass of the system?
Three
How far from the origin is the center of mass of the system?
Tap to reveal answer
To find the center of mass, we have to take the weighted average of the x coordinates and the y coordinates.
Measures: Measures
First, we take the weighted measurement of the x-axis:
We can see that the result of the x-axis contribution is equal to .
Now, let's look at the y-axis contribution:
This equals to
Now that we have the x and y components, we take the root of squares to get the final answer:
This will give us
To find the center of mass, we have to take the weighted average of the x coordinates and the y coordinates.
First, we take the weighted measurement of the x-axis:
We can see that the result of the x-axis contribution is equal to
Now, let's look at the y-axis contribution:
This equals to
Now that we have the x and y components, we take the root of squares to get the final answer:
This will give us
← Didn't Know|Knew It →
Doing which of the following would allow you to find the center of mass of an object?
Doing which of the following would allow you to find the center of mass of an object?
Tap to reveal answer
Center of mass can be found by spinning an object. It will naturally spin around its center of mass, due to the concept of even distribution of mass in relation to the center of mass. Shape and mass are important factors in this property, but the most improtant factor is the mass distribution.
Center of mass can be found by spinning an object. It will naturally spin around its center of mass, due to the concept of even distribution of mass in relation to the center of mass. Shape and mass are important factors in this property, but the most improtant factor is the mass distribution.
← Didn't Know|Knew It →
If two masses, and are placed on a seesaw of length , where must the fulcrum be placed such that the seesaw remains level?
If two masses,
Tap to reveal answer
This question asks us to find the center of mass for this system. We know that the center of mass resides a distance from the first mass such that:
In this case:
Plug in known values and solve.
This question asks us to find the center of mass for this system. We know that the center of mass resides a distance
In this case:
Plug in known values and solve.
← Didn't Know|Knew It →
If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?
If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?
Tap to reveal answer
Changing the position of the fulcrum by moving it to the left means the center of mass will be to the right of the new position. Therefore, the scale will tip right. Adding more mass to the left end will rebalance the scale. None of the other options make sense. Adding more mass to the new fulcrum position will not change the balance of the scale because that mass is a negligible distance from the new fulcrum position and does nothing to change the masses on either side.
Changing the position of the fulcrum by moving it to the left means the center of mass will be to the right of the new position. Therefore, the scale will tip right. Adding more mass to the left end will rebalance the scale. None of the other options make sense. Adding more mass to the new fulcrum position will not change the balance of the scale because that mass is a negligible distance from the new fulcrum position and does nothing to change the masses on either side.
← Didn't Know|Knew It →
Three point masses are at the points , and
and a point mass is at the point .
How far from the origin is the center of mass of the system?
Three
How far from the origin is the center of mass of the system?
Tap to reveal answer
To find the center of mass, we have to take the weighted average of the x coordinates and the y coordinates.
Measures: Measures
First, we take the weighted measurement of the x-axis:
We can see that the result of the x-axis contribution is equal to .
Now, let's look at the y-axis contribution:
This equals to
Now that we have the x and y components, we take the root of squares to get the final answer:
This will give us
To find the center of mass, we have to take the weighted average of the x coordinates and the y coordinates.
First, we take the weighted measurement of the x-axis:
We can see that the result of the x-axis contribution is equal to
Now, let's look at the y-axis contribution:
This equals to
Now that we have the x and y components, we take the root of squares to get the final answer:
This will give us
← Didn't Know|Knew It →