Download Lecture slides with notes

By the way…
α = “alpha”
ω = “omega”
θ = “theta”
τ = “tau”
Extra Practice: 8.1, 8.3, 8.5, 8.7, 8.25, 8.27
I’ve drawn a wrench but there’s a lot of physiotherapy application in this concept. So all you future physiologists, pay attention!
Movie project due TODAY!
• If you don’t have it now, deliver to my mailbox
in White Hall 111 by 4pm.
• Can be hand-written or computer (or both).
• Check through rubric before you finish the draft:
http://sarahspolaor.faculty.wvu.edu/home/physics-101
Will be 30% penalty if <week late, 50% penalty if 1-2 weeks late, 75% penalty if up to 2-3 weeks late. If not turned in by April 20 you will receive a 0.
Today’s goals.
• Calculate torque.
• Rotational equilibrium.
• Find something’s center of gravity.
Torque
The ability of a force to rotate an
object around an axis.
τ = rF⊥
Units: N m
r is a vector starting from axis of rotation
pointing to where force is applied
A FORCE at a given RADIUS makes a TORQUE. More torque means more rotational acceleration.
[See light board notes for examples]
Torque: Notes…
Convention:
Counterclockwise spin,
torque positive
+τ
!
F
Ex: wheel
with two
forces acting
on it
r
!
F
Net torque: an object can have a net torque acting on it even though the net force is zero.
Fnet = F - F = 0
tau_net = rF + rF = 2rF
We can have a net
torque even though
net force = 0!
Many problems will appear ugly (complicated). They’re not! Don’t get intimidated!
120 N
Identify:
1. Pivot point.
2. Line from pivot to force (r).
3. Force’s component
perpendicular to r.
The fishing pole in the figure makes an angle of 20.0° with
the horizontal. What is the magnitude of the torque exerted
by the fish about an axis through the angler's hand if the
fish pulls on the fishing line with a force of 120 N at an
angle 37.0° below the horizontal? The force is applied at a
point with distance L = 2 m from the angler's hands.
[Problem done on light board]
τ = rF⊥
Everyone grab something heavy. Is it harder to
hold it straight out or with your elbows bent?
A. Straight out
B. With elbows bent
C. Same for both
Q82
ANSWER: A.
You are using a wrench and trying to loosen a rusty
nut. Which of the arrangements shown is most
effective in loosening the nut?
τ = rF⊥
B.
A.
C.
D.
E. There are 2 best ones (equal torque)
Q83
SAY ANSWER: B.
Whenever I ask you a question like this, always consider your experience, but also consult the relevant equation!
Joe the plumber pushes
straight down on the end
of a long wrench as
shown. What is the
magnitude of the torque
Joe applies about the
pipe?
τ = rF⊥
19°
A. (0.80 m)(900 N) sin 19°
B. (0.80 m)(900 N) cos 19°
C. (0.80 m)(900 N) tan 19°
D. (0.80 m)(900 N)
E. None of the above
Answer: B
Q84
Equilibrium (again)
• Same concept as linear momentum.
• AT REST
• *OR* Rotating at CONSTANT VELOCITY!
ΣFx = 0
ΣFy = 0
Στ = 0
I’m just gonna say that in the next few lectures you’ll notice a common theme: that I’m going to keep saying, “this is just like we did before, only now for rotational
motion.” Previously we saw that kinematics equations have rotational equivalents, and here we are seeing that you need a torque to change rotation rate. Suggest
breaking this forces into x and y directions (one radial, other perpendicular). Like the fishing problem.
THESE EQUATIONS ARE THE DEFINITION OF EQUILIBRIUM!
Note, you’ve seen this before (with just forces, not torque) in linear equilibrium!
Center of Gravity
“Where should I draw my Fg line?”
The center of gravity is the point around which a body’s mass is equally distributed in all directions. Center of gravity answers a simple question but has practical
conceptual applications. For instance, if I throw something around what point will it rotate? Or, where should I put the fulcrum of my see-saw? If they were equal weight
it’d be in the middle, but since one kid is heavier it’s off to one side.
Center of Gravity
“Where should I draw my Fg line?”
Σmixi
xcg =
Σmi
60
kg
In a uniform object, COG is at its mid point
Center of gravity can be outside the object
Find the center of gravity of the system of
two blocks above if they are 50 m apart.
15 kg
Toppling Rule of Thumb
• If the CG of the object
is above the area of
support, the object
will remain upright.
• If the CG is outside
the area of support
the object will topple.
Leaning tower in Pisa, Italy
Try standing with your heels and butt against the wall and try to bend over. Can you keep standing? What’s happening to your center of gravity?
Human Center of Gravity
Within the body, near the navel
(Generally)
higher in men
than women
To avoid toppling - stand so that your center of
gravity is above area enclosed by your feet!