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perpendicular distance from the rotation axis to the line of action of F. In some problems this approach
may be easier than that of resolving the force into components.
If two or more forces are acting on a rigid object each has a tendency to produce rotation about a
pivot pointing. Thus we can say that the net torque acting on the rigid body about an axis through the
pivot point is (40)
From this definition of torque, we see that the rotating tendency increases as F increases and as d
increases.
2.11 Torque vs Force
Torque differs from force in a very important way. Torque is calculated or measured about a
pivot point. To say that a torque is 20 N is meaningless. You need to say that torque is 20 Nm about a
particular point. Torque can be calculated about any pivot point, but its value depends on the point
chosen. In practice, we measure or calculate torques about the same point from which we measure an
objects’ angular position θ (an thus its angular velocity ω and angular acceleration α). This assumption is
built into the equations of rotational dynamics.
2.12 The Rigid Body in Equilibrium
Now consider two forces of equal magnitude and opposite direction applied to a rigid object. The
force directed to the right tends to rotate the object clockwise about an axis perpendicular through the
pivot point, whereas the force directed to the left tends to rotate it counterclockwise about that axis.
Because the forces are of equal magnitude and act at the same perpendicular distance from the pivot
point, there torques are equal in magnitude. Therefore, the net torque on the rigid object is zero.
With no net torque, no changes occur in rotational motion and the rotational motion of the rigid
body remains in its original state. This is an equilibrium situation. We now have two conditions for
complete equilibrium on an object which can be stated as follows:
1. The net external force must equal zero: 0
2. (41) The net external torque must be zero about any axis: 0 (42) The first condition is a statement of translational equilibrium. The second condition is a statement
of rotational equilibrium. In the special case of static equilibrium, the object is at rest, so it has no
translational or angular speed. 9 Table 1: Moments of Inertia for Symmetrical Objects Rotating about One Axis http://www.vectorsite.net/tpecp_04.html 2.13 The Rigid Body under a Net Torque
Now let us consider the situation where the net torque on a rigid body is not zero. Just like with
Newton’s second law for translat...
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 Fall '09
 Physics, Angular Momentum, Moment Of Inertia, Rigid Body, Rotation

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