Transcript 8.2 Torque, Equilibrium, and Stability

Lecture Outline
Chapter 8
College Physics, 7th Edition
Wilson / Buffa / Lou
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Units of Chapter 8
Rotational Motion and Equilibrium
Rigid Bodies, Translations, and Rotations
Torque, Equilibrium, and Stability
Rotational Dynamics [Not tested on AP Physics B]
Rotational Work and Kinetic Energy [Not tested on
AP Physics B]
Angular Momentum [Not tested on AP Physics B]
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8.1 Rigid Bodies, Translations,
and Rotations
A rigid body is an object or a system of particles in
which the distances between particles are fixed (remain
constant).
Rigid bodies only exist in a perfect, IDEAL world!
In other words, a rigid body must be solid (but
not all solid bodies are rigid).
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8.1 Rigid Bodies, Translations,
and Rotations
A rigid body may have either two types of motion or
both:
1. Translational
2. Rotational
What’s the difference between the two?
You can combine both types of forces and that’s where
we get the term ROLLING!
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8.1 Rigid Bodies, Translations,
and Rotations
For an object that is rolling without slipping,
s = rθ
a = rα
An object can roll with slipping, but none of the
equations will hold when there is slipping.
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8.1 Rigid Bodies, Translations,
and Rotations
• A cylinder rolls on a horizontal surface without
slipping. The cylinder has a radius of 12 cm and
a center of mass speed of 0.10 m/s as it rolls
without slipping. If it continues to travel at this
speed for 2.0s, through what angle does the
cylinder rotate during this time?
8.2 Torque, Equilibrium, and Stability
The perpendicular distance from the line of
force to the axis of rotation is called the lever
arm or the moment arm. [symbol r, (like radius)
The product of the force and the lever arm is
called the torque.
S.I. Unit: m N
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8.2 Torque, Equilibrium, and Stability
Torque in rotational motion can be thought of
as the analogue of force in translational
motion.
Torque (rotational) is similar to Force (linear)
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8.2 Torque, Equilibrium, and Stability
Torque is a vector or scalar????
Counterclockwise is positive, and clockwise is
negative.
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8.2 Torque, Equilibrium, and
Stability
• In the human body torques
produced by the contraction of
muscles cause some bones to
rotate at joints. With the axis of
rotation through the elbow joint
and the muscle attached 4.0
cm from the joint, what are the
magnitudes of the muscle
torques for cases a and b if the
muscle exerts a force of 600 N.
8.2 Torque, Equilibrium, and Stability
In order for an object to be in equilibrium, the
net force on it must be zero, and the net torque
on it must be zero as well.
Equilibrium means that forces and torques are
in balance.
Can be at ______ or at _________ __________.
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8.2 Torque, Equilibrium, and Stability
• Two types of equilibrium:
– Translational
– Rotational
linear; forces
circular; torques
Mechanical Equilibrium
Static Equilibrium
8.2 Torque, Equilibrium, and Stability
Concurrent Forces vs. Couple
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8.2 Torque, Equilibrium, and Stability
• A picture hangs
motionless on a wall.
If the picture has a
mass of 3.0 kg, what
are the magnitudes of
the tension forces in
the wires?
8.2 Torque, Equilibrium, and Stability
• Three masses are
suspended from a
meter stick. How
much mass must be
suspended on the
right side for the
system to be in static
equilibrium? [Neglect
the mass of the meter
stick]
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8.2 Torque, Equilibrium, and Stability
If an object is in
stable equilibrium,
any displacement
from the equilibrium
position will create a
torque that tends to
restore the object to
equilibrium.
Otherwise the
equilibrium is
unstable.
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8.2 Torque, Equilibrium, and Stability
Whether equilibrium is stable or unstable
depends on the width of the base of support.
© 2010 Pearson Education, Inc.