Torque

1
Torque

• Torque in 2 and 3 dimensions

Text Sections 10.6
2
Torque is what causes rotation
An unbalanced force applied to an object causes
it to move (accelerate).
Even with no net force, the object is not
necessarily in equilibrium. A net torque will
cause it to rotate.
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A force directed toward the axis of rotation
produces no torque.
You cannot shut a door by pushing directly toward
the hinges (F1), or pulling directly away from
the hinges (F2).
hinge
F1
F2
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Divide the force vector into radial and
tangential components. Only the tangential
component produces a torque about the rotation
axis.
Torque (tangential force) ? (distance to
rotation axis)
(? is the angle between r and F )
r
Units Nm This is identical to the unit of
energy (joule), but is always called Nm when
it refers to torque.
Ft
?
Fr
F
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Another way to look at torque...
effective lever arm, r sin f
The shortest distance from the pivot to the line
of action of the force is the effective lever
arm. If the force were applied at right angles
to this shorter distance, the same torque would
result.
line of action of F
r
Torque (force) ? (effective lever arm)
?
F
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Torque as a vector
Vector product or cross product of 2 vectors
B?
B
?
A
Direction C is perpendicular to A and B (out of
the page, towards you). Right-hand rule
Fingers parallel to A when straight, and along B
as you curl them then the thumb gives the
direction of C. Not commutative!
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The cross-product is used to define torque as a
vector.
t
F
F
F
r
The direction of ? is along the axis about which
the body would tend to rotate. Right-hand rule
Thumb in direction of t, fingers indicate sense
of rotation.
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• Torque depends on
• The magnitude of the force
• The direction of the force
• The location at which the force is applied
• The point which you assume as the pivot or
  axis of rotation.

In two-dimensional problems, torque is either
clockwise or counterclockwise (we can take
one sense as positive, and the other as
negative). In 3-D, torque is a vector.
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Quiz
A weight W is placed at one end of a light plank.
What weight should be placed at the other end so
that the plank will balance on a pivot placed 1/3
of the way along the plank?
?
W

1. 3W
2. 2W
3. W
4. ½ W
5. 1/3 W

L/3
2L/3
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Each force produces a torque, t (tau), which
tends to rotate the plank about the pivot.
F
R
Torque is proportional to the force and to the
distance from the pivot torque
(length of lever) x (force)
(when the force is perpendicular to the lever
more complicated otherwise)
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Each force produces a torque, t (tau), which
tends to rotate the plank about the pivot. The
plank is in equilibrium when the torques are
equal and opposite.
Torque is proportional to the force and to the
distance from the pivot
torque (force) x (length of lever)
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Example
What is direction of rotation due to the 20N
force? What is direction of rotation due to the
25N force?
20 N
25 N
30 cm
40 cm
pivot
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Example
What is the torque due to the 20-N force? What is
the total torque?
20 N
25 N
30 cm
40 cm
pivot
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Example
A force F10N is applied to the end of a wrench
(of length L0.4m) in order to loosen a nut on a
bolt. The force is applied at an angle of 30 to
the wrench.
30
What is the torque applied to the nut?
F
L
Physics 1D03 - Lecture 10
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Example
A mass M is hanging from a string wrapped around
a massless wheel of radius R that is pivoted
through its center.
What is the torque applied to the wheel?
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Example
A mass M1 is hanging from a string wrapped around
a cylinder of radius R1 that is pivoted through
its center, and another mass M2, on a string
wrapped in the opposite direction, from a core
section protruding from the larger drum, at
radius R2. They cylinders are massless.
What is the torque applied to the cylinder?
Physics 1D03 - Lecture 10
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