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Chapter 8
Rotational Equilibrium
and
Rotational Dynamics
Force vs. Torque
Forces cause accelerations
Torques cause angular accelerations
Force and torque are related
Torque
The door is free to rotate about an axis through O
There are three factors that determine the effectiveness of the force in opening the
door:
The
magnitude
of the force
The
position
of the application of the force
The
angle
at which the force is applied
Torque, cont
Torque, , is the tendency of a force to rotate an object about some axis
= r F
is the torque
F is the force
symbol is the Greek tau
r is the length of the position vector
SI unit is N
.
m
Direction of Torque
Multiple Torques
When two or more torques are acting on an object, the torques are added
As vectors
If the net torque is zero, the object’s rate of rotation doesn’t change
General Definition of Torque
The applied force is not always perpendicular to the position vector
The component of the force
perpendicular
to the object will cause it to rotate
General Definition of Torque, cont
When the force is parallel to the position vector, no rotation occurs
When the force is at some angle, the perpendicular component causes the rotation
General Definition of Torque, final
Taking the angle into account leads to a more general definition of torque:
n r F sin
F is the force
r is the position vector
±
is the angle between the force and the position vector
Lever Arm
The
lever arm
, d, is the perpendicular distance from the axis of rotation to a line
drawn along the direction of the force
d = r sin
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View Full DocumentRight Hand Rule
Point the fingers in the direction of the position vector
Curl the fingers toward the force vector
The thumb points in the direction of the torque
Net Torque
The net torque is the sum of all the torques produced by all the forces
Remember to account for the direction of the tendency for rotation
Counterclockwise torques are positive
Clockwise torques are negative
Torque and Equilibrium
First Condition of Equilibrium
The net external force must be zero
This is a necessary, but not sufficient, condition to ensure that an object is in
complete mechanical equilibrium
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 Winter '08
 Jacobs
 Acceleration, Force

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