with illustration and seatwork

1. *door top view F1
F2
axis of rotation r1
r2
Where:
F = force
r = lever arm=
perpendicular
distance from
the axis of
rotation to the
line along which
the forces acts.
here.,
α∝ F

2. *door top view F1
F2
axis of rotation r1
r2
α ∝ F x r Moment of Force or Torque (τ)
α ∝ τ

3. a vector quantity that determines
the ability of a force to introduce
rotation.
τ = rF ; unit: mN
1.Magnitude of the applied force
2.Distance from point of application to
pivot (location of applied force)
3.Angle ( direction of the applied force)

4. F1
F2
F3
r1
r2
τ F1 > τ F2
τ F2 < τ F1
τ = 0
NOTE: in general τ = r⊥F
Remind us that we must
use the distance from
the axis of rotation that
is perpendicular to the
line of action of the
force
r⊥ = r sin
ⴱ

5. F2
ⴱ
τ = rF⊥
l = rF⊥ sinⴱ
We can use τ = r⊥ F or τ = r F⊥ or τ = r F sin ⴱ
to calculate the torque whichever is easiest.
Line of action of a force - the line of motion of a
force is an imaginary line of indefinite length drawn a
long the direction of the force
The moment arm  is the perpendicular distance
from the line of action of a force to the axis of
rotation.

6. 1. An 80 N acts at the end of a 12 cm wrench
as shown. Find the torque.
80 N
12 cm
ⴱ =60o
2. Find the resultant torque about axis A for
the arrangement shown:
ⴱ =30o
ⴱ =30o
4 m
2 m6 m
F3 =20 N
F2 = 40N
F1 =30 N

7. Torque is a vector quantity that has a direction as
well as magnitude
Thumb  F (force)
Pointer  r (moment arm)
Middle finger  direction
of τ (torque)

9. ↑ Up +
↓ Down -
→ Right +
← left -
⊙ Outward +
⊗ Inward -
CC Counterclockwise +
C clockwise -

10. → ⊗ ↑
← ⊙
⊙ →
↑
↑

11. Car at rest Constant speed, no
change in direction
An object is said to be in equilibrium if it does
not have linear acceleration and angular
acceleration
Linear acceleration is Zero if….

12. Angular acceleration is Zero if….
wheel at rest Constant rotation

15. The center of mass lies at the
geometric center for a
symmetric, uniform density
object.
h/3
h
R
h/2
h
h/2
h

16. The center of mass can be
outside the mass of the body.
Center of mass

17. Ability of an object to return to its
original position after it is displaced or
tilted slightly
- CG is below of point of support
- the objects return to its original position
- When object is displaced, the object moves
even farther from its position
- When object is displaced, the object remain
in its position

21. cm