Torque and Equilibrium
Torque
What exactly is torque in normal English?
 Rotational
effect of force. Tells how
effective force is at twisting or rotating
an object.
tnet = I α
t
= +- r Fperpendicular = r F sin q
Units N m
Sign, CCW rotation is (usually) positive
Why is there a sine theta in the Torque equation!?!!??!
07
Question
The picture below shows three different ways of
using a wrench to loosen a stuck nut. Assume the
applied force F is the same in each case.
In which of the cases is the torque on the nut the
biggest?
A. Case 1
B. Case 2
C. Case 3
10
Question 2
The picture below shows three different ways of
using a wrench to loosen a stuck nut. Assume the
applied force F is the same in each case.
In which of the cases is the torque on the nut the
smallest?
A. Case 1
B. Case 2
C. Case 3
12
Torque Example
A person raises one leg to an angle of 30 degrees. An ankle
weight (89 N) attached a distance of 0.84 m from her
hip. What is to torque due to this weight?
30
F=89 N
If she raises her leg higher, the torque due to the weight will
A) Increase
B) Same
C) Decrease
17
Equilibrium
A
rod is lying on a table and has two equal but
opposite forces acting on it, one on each end.
What is the net force on the rod?
A) Up
B) Down
C) Zero
 Will
the rod move? A) Yes B) No
F
y
x
F
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Equilibrium
 Conditions
for Equilibrium
S F = 0
Translational EQ (Center of
Mass)
S t = 0
Rotational EQ
» Can choose any axis of rotation…. Choose
Wisely!
25
Example: Equilibrium
A meter stick is suspended at the center. If a 1 kg
weight is placed at x=0. Where do you need to
place a 2 kg weight to balance it?
50 cm
9.8 N
d
19.6 N
25
Question
The picture below shows two
people lifting a heavy log.
Which of the two people is
supporting the greatest weight?
1. The person on the left is
supporting
the greatest weight
2. The person on the right is
supporting
the greatest weight
3. They are supporting the same
weight
33
Example: hanging beam
2m
A 40kg uniform beam is being
supported by two ropes. What
is the tension in each rope?
40kg
3m
Example: painter
A painter of mass 50kg uses two supports and a
plank of mass 20kg as a platform to paint his
house.How far to the right of support B can
the painter stand before the plank tips?
3 meter
1 meter
1 meter
20kg
A
B
Just before board tips, force from A becomes zero
47
Example: continued
3 meter
1 meter
1 meter
20kg
A
B
Example: falling beam
2m
If the right rope breaks, what
is the initial angular
acceleration of the beam?
40kg
3m
Example: Rolling

An hoop with mass M, radius R, and moment
of inertia I = MR2 rolls without slipping down
a plane inclined at an angle q = 30o with
respect to horizontal. What is its acceleration?

Consider CM motion and rotation about
the CM separately when solving this
problem
I
M
R
q
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Rolling...
Static friction f causes rolling. It is an
unknown, so we must solve for it.
 First consider the free body diagram of the
object and use
 In the x direction


Now consider rotation
about the CM
and use t = I
M
R
f
Mg
q
q
33
Rolling...

We have two equations:

We can combine these to eliminate f:
I
A
M
R
q
36
Summary
 Torque
= Force that causes rotation
tnet = I α
t = F r sin q
Work done by torque W = t q
 Equilibrium
S F = 0
S t = 0
» Can choose any axis.
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