centre of mass

1. *

2. *Know what the turning effect of
a force is
*Know that the moment of a
force depends on force and the
distance from the pivot
*Know the principle of moments

3. *
Where do you push?
Hi, my
name is
Mr Stick
hinges

4. *
I can’t do
it!

5. *
That’s
easier!

6. *
The size of the force
Obviously!

7. *
The distance from the pivot (axis of rotation)
Not quite
so obvious!
Axis of rotation

8. The turning effect of a force is called the moment of the
force
The moment is calculated by multiplying the force by the
distance from the pivot

9. *
Moment (Nm) = Force (N) x distance from pivot
(m)
Note the unit is Nm, not N/m!

10. The force which you apply to a spanner to undo a tight nut is called
a TURNING FORCE.
The longer the handle of the spanner then the greater is the turning
effect of the force.
Force producing a turning force to loosen the nut.

11. A spanner is an example of a FORCE MULTIPLIER.
Another example of a force multiplier is a crow bar.
Effort
LoadFulcrum

12. Another example of a force multiplier is a wheelbarrow.
Effort
Load
Fulcrum

13. A spanner is an example of a FORCE MULTIPLIER.
Another example of a force multiplier is a crow bar.
Effort
LoadFulcrum
Here it is being used to lift a heavy load and
force being applied is called the effort.
The effort required to lift the load is only a
fraction of its weight.
A turning force is being applied about the PIV
Or FULCRUM

14. The MOMENT of a TURNING FORCE is defined as
“the product of the force and the perpendicular distance
of its line of action from the pivot”.
d
d
F F
s
Moment of F = F x d Newton Metres(Nm)
Moment of F = F x s Newton Metres (Nm
Line of action of
F

15. *Balancing unequal masses are again about centre of mass
*For example,
*The bus is heavier than the car so they’re not in balance.d1
M1
M2
d2

16. *In order to balance the system, we should change their
distances to the support.
*Now they’re in balance.
m1.d1=m2.d2
d2d1

17. When more than one force is applied to a pivoted object it is possible
For a small force to balance a large force provided that each force has
EQUAL but OPPOSITE moments.
The following experiment allows us to investigate the PRINCIPLE
OF MOMENTS:
“For an object in a state of equilibrium the
sum of the clockwise
moments taken about a point is equal to the
sum of the anticlockwise
moments taken about the same point.”

18. W2 W3 W4W1
d1
d2 d3
d4
W1 & W2
produce anti-clockwise
moments
W3 & W4
produce clockwise
moments

19. From the results we can see that the sum of the clockwise moments
and the sum of the anticlockwise moments are equal when the lever
is balanced (in equilibrium).
Example:
Find the value of the missing force in the following example if the
lever is in equilibrium.

20. Find the value of the missing force in the following example if the
lever is in equilibrium.
5N W10N
0.5m
0.25m
0.8m

21. Find the value of the missing force in the following example if the
lever is in equilibrium.
5N W10N
0.5m
0.25m
0.8m
If the object is in a state of equilibrium then:
Anti Clockwise Moments = Clockwise Moments
(10 x 0.5) + (5 x 0.25) = W x 0.8
5 + 1.25 = 0.8W
6.25 = 0.8W
W = 6.25/0.8
= 7.8 Newtons (2 sig figs)

22. *

23. *
*The small forces act like a single force at G. This means
that they have the resultant force at G.
*The resultant force is the stick’s weight.
*G is the centre of mass.
*

24. *
*Centre of mass of a body is the body that moves as though
all of the mass were applied there.

25. *If the object is uniform, for example a meter stick, the
center of mass will be at the exact geometric center.
*But, if the shape is irregular we use plumb line.
*Draw lines from each vertex along the plumb line by
assuming that the point is on that line
*After drawing the lines the centre of the mass will be
on the intersection point of these lines.
Intersection point-
Centre of mass
G

26. *But, if the shape is irregular we use plumb line.
*Draw lines from each vertex along the plumb line by
assuming that the point is on that line
*After drawing the lines the centre of the mass will be
on the intersection point of these lines.
Plumb line
Intersection point-centre
of mass

27. *
*If an object isn’t moving and remainig same, the object is
stable.
* State of rest or balance due to the equal action of opposing
forces is called equilibrium.
*When the object is stable it’s also in equilibrium which
means the forces acting on the object and the forces
turning effects are in balance.

28. *
Will turn to
its original
position
Small
force will
turn it over
Will definetely fall
over before another
force is applied

29. *
*There are three states of equilibrium,

30. *
*The objects that have wide base also have the lower centre
of mass.
*The lower the centre of mass is, the more stable object is.
*So it’s more difficult to fall over an object with wider base.

31. *
*The objects that have very little base, have high centre of
mass.
*And if these objects are tilted the centre of mass
immediately passes beyond the base.
*So they’re not stable and it’s easy to fall these objects over.

32. *
*The objects that are in neutral equilibrium stay where
they’re lefted.
*When moved, it changes the position.
*Wherever they stay, their center of mass is always over
their base.

33. *
*The center of mass of a two-particle system lies on the line
connecting the particles (or, more precisely, their individual
centers of mass). The center of mass is closer to the more
massive object
*The center of mass of a ring is at the center of the ring (in
the air).

35. *
*The center of mass of a solid triangle lies on all three
medians and therefore at the centroid, which is also the
average of the three vertices.

36. *
*Objects rotate around their center of mass
*In a uniform gravitational field, the center of
mass and center of gravity are the same.
*A projectile’s center of mass will follow a
parabolic path.
*If an object’s center of mass is outside it’s base
of support, it will topple.
*An applied force that is not through an object’s
center of mass will cause rotation.