Engineering Mechanics 1 - Lecture 2: Moment of a Force

Practice flashcards covering the concepts, formulas, and specific calculation examples for Moments of a Force from Engineering Mechanics 1, Lecture 2.

What is the definition of the 'moment of a force' (torque)?

A tendency for a body to rotate about a point that is not on the line of action of the force when a force is applied to that body.

What is the formula for the magnitude of a moment $M_O$?

$$M_O = Fd$$

What is the formula for the resultant moment $(M_R)_O$ of a system of forces?

$$M_{Ro} = \sum F_i d_i$$

In the example on Page 4, what is the moment $M_O$ for a force of $100\,N$ at a distance of $2\,m$?

$$M_O = (100\,N)(2\,m) = 200\,N \cdot m$$

For a force of $7\,kN$ acting at a point such that the distance to point $O$ is calculated as $(4\,m - 1\,m)$, what is the moment $M_O$?

$$M_O = (7\,kN)(4\,m - 1\,m) = 21.0\,kN \cdot m$$

According to the example on Page 5, what is the total resultant moment $M_{Ro}$ of the four forces acting on the rod?

$$M_{Ro} = 334\,N \cdot m$$

What formula is used to find the magnitude of the resultant force $F_R$?

$$F_R = \sqrt{(F_{Rx})^2 + (F_{Ry})^2}$$

How is the direction $\theta$ of the resultant force determined?

$$\theta = \tan^{-1}\left(\frac{|(F_R)_y|}{|(F_R)_x|}\right)$$

In the equivalent system problem (Page 8), what are the calculated components $\sum F_x$ and $\sum F_y$?

$\sum F_x = 5.598\,kN$ and $\sum F_y = -6.50\,kN$

What is the magnitude of the resultant force $F_R$ in the system replacement example on Page 8?

$$F_R = \sqrt{(5.598\,kN)^2 + (6.50\,kN)^2} = 8.58\,kN$$

In the final example on Page 9, what is the calculated value for the direction angle $\theta$?

$$\theta = 49.3^\circ$$

What is the resultant couple moment $(M_R)_O$ calculated in the equivalent system example?

$(M_R)_O = -2.46\,kN \cdot m = 2.46\,kN \cdot m$ (clockwise)

For the angle bracket with $F = 400\,N$ at $30^\circ$, what was the final moment calculation about point $O$?

$M_O = -98.6\,N \cdot m = 98.6\,N \cdot m$ (clockwise)