Free Practice Quiz Question List

3 Moments and Couples Online Quiz Questions

Use this free practice quiz with 20 questions to review 3 Moments and Couples, test your knowledge, and prepare for your next test or exam.

20 questions

True or false

1 point

True or false: A force whose line of action passes through reference point $O$ has zero moment about $O$ .

A
True
B
False

Choose one

1 point

A force of magnitude $F$ acts at a perpendicular distance $d$ from a reference point. Which expression gives the magnitude of its moment about that point?

A
$F/d$
B
$Fd$
C
$F+d$
D
$d/F$

Fill in the blank

1 point

In a two-dimensional problem, $\mathbf{r}=(0.20,0.60)\,\text{m}$ and $\mathbf{F}=(10,4)\,\text{N}$ . Using counterclockwise as positive, calculate the signed moment about $O$ in $\text{N·m}$ :

Choose one

1 point

For $\mathbf{r}=(1,0,2)\,\text{m}$ and $\mathbf{F}=(0,3,0)\,\text{N}$ , what is the moment vector $\mathbf{r}\times\mathbf{F}$ ?

A
$(6,0,-3)\,\text{N·m}$
B
$(-6,0,3)\,\text{N·m}$
C
$(0,-6,3)\,\text{N·m}$
D
$(-6,3,0)\,\text{N·m}$

Written response

1 point

Which rule determines the direction of the moment vector produced by a three-dimensional cross product?

True or false

1 point

True or false: The two forces in a couple have zero resultant force, while still producing a moment.

A
True
B
False

Fill in the blank

1 point

Two opposite parallel forces of magnitude $25\,\text{N}$ have lines of action separated by $0.40\,\text{m}$ perpendicularly. The couple magnitude is $\text{N·m}$ .

Choose all

1 point

Select all statements that correctly describe a couple.

A
A couple consists of equal, opposite, parallel forces on distinct lines.
B
The resultant force of a couple is zero.
C
The magnitude of a couple moment is $Fd$ , where $d$ is the perpendicular separation of the force lines.
D
A couple moment is independent of the reference point.
E
A couple has a nonzero resultant force equal to twice either force’s magnitude.

Written response

1 point

A moment vector is $\mathbf{M}=(4,-7,2)\,\text{N·m}$ . The unit direction of an axis is $\mathbf{u}=(0,\frac{3}{5},\frac{4}{5})$ . Calculate the signed scalar moment about that axis. Enter the value in N·m.

Choose all

1 point

Select all statements that are valid checks when calculating or summing moments.

A
Use $\mathbf{r}\times\mathbf{F}$ , with $\mathbf{r}$ drawn from the moment center to the force’s line of action.
B
Keep coordinate signs consistent with a right-handed coordinate system.
C
Include both force moments and applied couples when summing moments.
D
A moment has units of force times distance but is not energy.
E
Use $\mathbf{F}\times\mathbf{r}$ to calculate the moment of a force.

Choose one

1 point

A force is resolved into components to calculate its moment about a point. According to Varignon’s theorem, how should the component moments be combined?

A
The force’s components must be parallel to each other.
B
The moment of each component must be converted into energy before adding.
C
The moments produced by the force’s components can be added algebraically.
D
Only the largest force component contributes to the moment.

Open ended

1 point

A force $\mathbf{F}=(3,-2,4)\,\text{N}$ acts at position vector $\mathbf{r}=(2,1,-1)\,\text{m}$ from point $O$ . Calculate the moment vector about $O$ and its magnitude. Show the component calculations.

True or false

1 point

True or false: A moment and energy can share the unit dimensions $\text{N·m}$ , but a moment is not energy.

A
True
B
False

Written response

1 point

A moment vector has components $\mathbf{M}=(6,-8,0)\,\text{N·m}$ . Calculate its magnitude and enter the value in N·m.

Choose one

1 point

For calculating the moment of a force about reference point $O$ , which description correctly defines the position vector $\mathbf{r}$ ?

A
From the reference point to any point on the force’s line of action
B
From the force’s line of action toward the reference point
C
Parallel to the force, with its tail at the reference point
D
From the reference point to the body’s center of mass

Choose one

1 point

Which statement correctly distinguishes a moment from energy?

A
A moment is energy because both quantities have units of N·m.
B
A moment has units of N/m, so it cannot be compared with energy.
C
A moment has units of N·m, but it is not energy.
D
A moment has units of N·m only when it is a couple; otherwise it has units of N.

Choose one

1 point

Two equal, opposite, parallel forces act along distinct lines and form a couple. How does the couple moment depend on the reference point?

A
Its moment changes with the choice of reference point, just like the moment of a single force.
B
Its moment is independent of the choice of reference point.
C
Its moment is zero about every reference point.
D
It can be represented only at the midpoint between the two force lines.

Written response

1 point

What theorem states that a force’s moment can be found by summing the moments of its components algebraically?

Choose one

1 point

A force $\mathbf{F}=(30,-50)\,\text{N}$ acts at position $\mathbf{r}=(0.40,0.20)\,\text{m}$ from $O$ . Using counterclockwise as positive, what is the signed $z$ -component of the moment about $O$ ?

A
$-26\,\text{N·m}$
B
$26\,\text{N·m}$
C
$-14\,\text{N·m}$
D
$14\,\text{N·m}$

Choose one

1 point

Given $\mathbf{r}=(1,2,0)\,\text{m}$ and $\mathbf{F}=(0,0,10)\,\text{N}$ , what is the moment vector $\mathbf{M}_O=\mathbf{r}\times\mathbf{F}$ ?

A
$(-20,10,0)\,\text{N·m}$
B
$(20,-10,0)\,\text{N·m}$
C
$(0,0,20)\,\text{N·m}$
D
$(10,20,0)\,\text{N·m}$