1. Lecture 15 Physics 111 Results from Exam #2
Chapter 8: Rotational Equilibrium and
Rotational Dynamics
Monday, October 26, 1998
Physics 111

2. The Physics 111
Help Session
None This Week
Mondays
5:00 - 6:30 pm
8:00 - 9:00 pm
NSC Room 118

3. Exam 2 Generally, most of you did better this time!
The grading has been completed. However,
there are still a couple of students who have
not completed the exam yet. So, I will return
them on Wednesday.
If you’re dying to know how you did, stop by
my office--I have scores for those of you who
took the exam.

4. D C B A
If I had to
put letter
grades on
this exam...

5. Chapter 8 Rotational Dynamics
We’ve already started down this path, looking
at the motion of objects that rotate. We’re
now going to formalize and generalize the
types of motion we consider using a few
new concepts.

6. Let’s look at a balance scale...X?
10 g
50 g
If I hang a 10 g mass at
the end of the left side
of the balance...
…where should I hang
the 50 g mass to get
the scale to balance?

7. How did we arrive at such an answer?
10 g L
50 g
L/5
How did we arrive at such an answer?
Perhaps we used one of these formulae:

8. Let’s restate our balance condition so that we
10 g L
50 g
L/5
Let’s restate our balance condition so that we
get all the subscript 1’s on the same side and
all the subscript 2’s on the same side...

9. 98 L = 98 L L/5 L So in the case of this balance, we have...
10 g L
50 g
L/5
So in the case of this
balance, we have...
98 L = 98 L
Good! The balance is in balance!

10. The scale rotates around the pivot point.
5 g L
50 g
L/5
What happens to our balance if I change the
mass on the left side from 10 g to 5 g?
5 g L
50 g
L/5
The scale
rotates around
the pivot point.

11. X = L/2 Let’s look at one more case with our balance... L L X?
10 g L L
5 g
10 g X?
Now where should I hang the 10 g mass to
get the scale to balance?
How did we arrive at
this answer?
X = L/2

12. First, we examined the left side of the balance:
10 g L X?
5 g
First, we examined the left side of the balance:
Then, we examined the right side:

13. If the scale is balanced, the two sides should equal one another:
10 g L X?
5 g
If the scale is balanced, the two sides should
equal one another:

14. In our scale experiments, we’ve been playing
around with a physical quantity that we’ve not
yet encountered formally.
Our experiments show us that this quantity is
related to a force applied at a distance.
The farther away from the pivot point the
force is applied, the greater our new quantity is.
When present and unbalanced, our new physical
quantity cause the scale to rotate in the direction
of the unbalanced force.

15. We’ve also seen that the quantity is additive.
That is, if we have two forces on one side of
the pivot at two different distances, the resulting
physical quantity is simply the sum of the two
force * distance products.
Before we name our new physical quantity, let’s
examine one more thought experiment.

16. Let’s put a mass on one side of our balance and let go.
What will eventually happen to this system?
(Assume there is SOME friction in the pivot,
but that the pivot is free to rotate 360o.)

17. The mass eventually comes to rest with the balance aligned vertically.
We still have a mass
of 50 g at a distance
L from the pivot point,
so why has the motion
stopped? What has
happened to the value
of our new physical
quantity?

18. that the gravitational force on the mass is acting along
For this case, we notice
that the gravitational force
on the mass is acting along
the length of the balance.
50 g L
In other words, the force
is parallel to the radius of
length L around the pivot
point.
In this case, the magnitude
of our new physical quantity
must be

19. Torque Let’s finally give a name to this new physical quantity.
How about...
Any suggestions?
Torque
Where d is the distance from the pivot point (the
point of rotation) to the point at which the force
is applied and
is the component of the applied
force that is perpendicular to the
line joining the pivot point to the
point at which the force is applied.

20. Units! Although this has the same units as energy (J),
we generally denote torques as forces acting at
a distance, and therefore leave the units in the
form N m.

21. 0.5 m What is the magnitude of the torque experienced
pivot
What is the
magnitude of the
torque experienced
by this unbalanced
balance? Fg
Here, the force of
gravity acts
perpendicularly
to the radius joining
the two blue points
above.

22. f = 30o 0.5 m In this case, the force of gravity is NOT
pivot
50 g
0.5 m
In this case, the force
of gravity is NOT
perpendicular to the
line joining the two
blue points. Fg
f = 30o
Only the component
of Fg that acts
perpendicularly to
this line will cause
torque. Fg

23. f = 30o
pivot
50 g
0.5 m Fg

24. Concept Quiz!
Torque