3 Moments and Couples Free Online FlashCards

What does a moment measure?

A moment measures the rotational effect of a force about a point or axis.

What is a force’s moment if its line of action passes through the reference point?

The moment is zero because the perpendicular distance from the point to the force’s line of action is zero.

What sign convention is used for planar moments?

Counterclockwise moments are positive, and clockwise moments are negative.

How do you determine the direction of a three-dimensional moment?

Use the right-hand rule to determine the direction of the moment vector.

What forces make up a couple, and what is their net force?

A couple is a pair of equal, opposite, parallel forces acting along distinct lines. Their resultant force is zero, but they produce a moment.

How does a couple moment depend on the reference point?

A couple moment is independent of the reference point, so it is a free vector that can be added directly to other moments.

How do you calculate a force’s moment about point $O$?

The moment about point $O$ is $\mathbf{M}_O=\mathbf{r}\times\mathbf{F}$, where $\mathbf{r}$ runs from $O$ to any point on the force’s line of action.

How can you calculate a force moment’s magnitude?

Its magnitude is $|\mathbf{M}_O|=rF\sin\theta=Fd$, where $\theta$ is the angle between $\mathbf{r}$ and $\mathbf{F}$, and $d$ is the perpendicular distance to the force’s line of action.

What is the $z$-component formula for a planar moment?

For axes with $x$ to the right and $y$ upward, the moment’s $z$-component is $M_{O,z}=r_xF_y-r_yF_x$.

How do you find a 3D moment vector’s magnitude?

The magnitude is $|\mathbf{M}_O|=\sqrt{M_x^2+M_y^2+M_z^2}$, using the three components of the moment vector.

How do you find a moment about a specified axis?

Project the moment vector onto the axis: $M_{\text{axis}}=\mathbf{u}\cdot\mathbf{M}_O$, where $\mathbf{u}$ is a unit vector along that axis.

How do you calculate a couple’s moment magnitude?

A couple’s moment magnitude is $M_c=Fd$, where $F$ is the force magnitude and $d$ is the perpendicular separation between the forces’ lines of action.