### All AP Physics C Electricity Resources

## Example Questions

### Example Question #4 : Rotational Motion And Torque

A particle is moving at constant speed in a straight line past a fixed point in space, c. How does the angular momentum of the particle about the fixed point in space change as the particle moves from point a to point b?

**Possible Answers:**

It cannot be determined without knowing the mass of the particle

The angular momentum increases

The angular momentum does not change

The particle does not have angular momentum since it is not rotating

The angular momentum decreases

**Correct answer:**

The angular momentum does not change

The angular momentum of a particle about a fixed axis is . As the particle draws nearer the fixed axis, both and change. However, the product remains constant. If you imagine a triangle connecting the three points, the product represents the "of closest approach", labeled "" in the diagram.

### Example Question #1 : Understanding And Finding Center Of Mass

Doing which of the following would allow you to find the center of mass of an object?

**Possible Answers:**

Sliding it along a flat surface

Hanging it from a fixed point

Spinning it

Recording its shape

**Correct answer:**

Spinning it

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.

### Example Question #2 : Understanding And Finding Center Of Mass

If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?

**Possible Answers:**

Apply the same amount of mass to both ends

Apply more mass to the right end

If the scale was initially balanced, moving the fulcrum will not change this

Apply more mass to the new position of the fulcrum

Apply more mass to the left end

**Correct answer:**

Apply more mass to the left end

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.

### Example Question #3 : Understanding And Finding Center Of Mass

If two masses, and are placed on a seesaw of length , where must the fulcrum be placed such that the seesaw remains level?

**Possible Answers:**

**Correct 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.

### Example Question #4 : Understanding And Finding Center Of Mass

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?

**Possible Answers:**

**Correct 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

### Example Question #5 : Rotational Motion And Torque

An object starts from rest and accelerates to an angular velocity of in three seconds under a constant torque of . How many revolutions has the object made in this time?

**Possible Answers:**

**Correct answer:**

Since it is experiencing a constant torque and constant angular acceleration, the angular displacement can be calculated using:

The angular acceleration is easily calculated using the angular velocity and the time:

Using this value, we can find the angular displacement:

Convert the angular displacement to revolutions by diving by :

### Example Question #1 : Rotational Motion And Torque

A circular disk of radius 0.5m and mass 3kg has a force of 25N exerted perpendicular to its edge, causing it to spin. What is the angular acceleration of the disk?

**Possible Answers:**

**Correct answer:**

We can find the angular acceleration using the rotaional motion equivalent of Newton's second law. In rotational motion, torque is the product of moment of inertia and angular acceleration:

The moment of inertia for a circular disk is:

The tourque is the product of force and distance (in this case, the radius):

We can plug these into our first equation:

Simplify and rearrange to derive an equation for angular acceleration:

Use our given values to solve:

### Example Question #1 : Using Torque Equations

A meter stick is nailed to a table at one end and is free to rotate in a horizontal plane parallel to the top of the table. Four forces of equal magnitude are applied to the meter stick at different locations. The figure below shows the view of the meter stick from above.

You may assume the forces and are applied at the center of the meter stick, and the forces and are applied at the end opposite the nail.

What is the relationship among the magnitudes of the torques on the meter stick caused by the four different forces?

**Possible Answers:**

**Correct answer:**

Torque is given by,

Since all of the forces are equal in magnitude, the magnitude of the torque is then influenced by the radius* r* and the angle theta between the radius and the force.

For ,

For ,

For ,

For ,

Combining this information yields the relationship,

### Example Question #2 : Using Torque Equations

A man sits on the end of a long uniform metal beam of length . The man has a mass of and the beam has a mass of .

What is the magnitude of the net torque on the plank about the secured end of the beam? Use gravity .

**Possible Answers:**

**Correct answer:**

The net torque on the beam is given by addition of the torques caused by the weight of the man and the weight of the beam itself, each at its respective distance from the end of the beam:

Let's assign the direction of positive torque in the direction of the torques of the man's and the beam's weights, noting that they will add together since they both point in the same direction.

We can further simplify by combining like terms:

Using the given numerical values,

### Example Question #3 : Using Torque Equations

Two children sit on the opposite sides of a seasaw at a playground, doing so in a way that causes the seasaw to balance perfectly horizontal. The child on the left is from the pivot.

What is the mass of the second child if she sits from the pivot?

**Possible Answers:**

**Correct answer:**

A torque analysis is appropriate in this situation due to the inclusion of distances from a given pivot point. Generally,

This is a static situation. There are two torques about the pivot caused by the weights of two children. We will note that these weights cause torques in opposite directions about the pivot, such that

Consequently,

Or more simply,

Solving for ,

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