The document discusses the concepts of force and moment in mechanics, defining force as the change in an object's state and moment as the intensity of a turning effect. It includes details on force visualization, component representation, and calculations related to these physical quantities. Key units mentioned are newtons (n) for force and newton-meters (n·m) for moment.

1. Force & Moment
1. Force
Goal
2. Moment
1/11

2. Force
Force is changes object state
Move Deformation
Unit ：N (Newton)
F：
Vector magnitude & direction：
2/11

3. Force Visualization by Arrow
Direction ： direction of force
Length ： Intensity of force
Visualization of applied forces is
the first and important step
to solve problems.
3/11

4. Component Representation
x
y
F =
Fx
Fy
F
Fy
Fx
Component is scalar.
|F| cos θ
θ
-|F|sin θ
=
|F| cos θ
-|F|sin θ
4/11

5. Force Representation
in Mechanics of Materials
F F
Symbol F ： Component
Tension load
F F
Compression load
x
y
5/11

6. Moment of Force → Moment
Intensity of turning effect of a forceM：
M ＝ r × F
Axis
F
r
Unit ：N・m
Vector magnitude & direction：
6/11

7. Moment Visualization by Arrow
Direction
Length
：
：
Axis
Intensity
M
Right hand screw direction is positive.
7/11

8. Component Representation
M
Fx
Fy
Fz
x
y
×
rx
ry
rz
Mx
My
Mz
=
ry Fz rz Fy
rz Fx rx Fz
rx Fy
ry Fx
=
Axis
F
r
8/11

9. 2 Dimension (x-y plane) Case
0
rx Fy
ry Fx
0=
Mx
My
Mz
ry Fz rz Fy
rz Fx rx Fz
rx Fy
ry Fx
= F
r
M
x
y
rx
ry
Fy
Fx
9/11

10. Q. Moment ?
axis F1
r1
Mx
y
r1 (-F1) - 0 ・ 0M =
= - r1 F1
10/11

11. Summary
1. Force
2. Moment
Force is changes object state
Unit ：N (Newton)
F：
Intensity of turning effect of a forceM：
M ＝ r × F
Unit ：N・m
11/11