http://www.ck12.org Chapter 8. Angular Motion and Statics
8.2 Torque
Vocabulary
- axis of rotation: A line drawn perpendicular to the plane of the object’s rotation through the point about
which the object rotates. - lever arm and moment arm:The handle/arm of a wrench.
- rigid bodies:Objects that do not undergo any deformation when subject to a force (or forces). Rigid bodies
are in an idealized state. - torque:The component of a force applied perpendicular to a lever arm. Torque is the product of the length
of a lever arm and the force applied perpendicular to a lever arm. Torque is a scalar quantity and can have
clockwise or counter-clockwise direction.
Rigid Bodies and Torque
We define arigid bodyas an object that does not undergo any deformation when subjected to a force (or set of
forces). This is an idealized state since all objects deform a bit under the application of any force. Even a block of
steel resting on a slab of concrete is deformed slightly by the force of gravity- it tends to flatten. But unless the block
is subject, for example, to a huge compressive force, the amount of deformation (flattening) is considered negligible
under “normal” conditions, and the block is assumed a rigid body. With the introduction of rigid bodies, we also
remove the restriction that the forces experienced by such bodies are applied at their geometric center.
We will now consider forces applied at any point. For example, we might be asked to describe the resulting motion
of a meter stick resting on a frictionless tabletop that is subject to a forceFapplied at its 10-cm mark, as inFigure
8.2. How do you think the meter stick will move? What does experience or intuition tell you? Even though we do
not have a frictionless tabletop in our possession, we can certainly imagine what the motion would be like. Did you
guess the meter stick would rotate about its center? The off-center forceFinFigure8.2 causes the stick to rotate
about this point (we will ignore any possible translation).
A line drawn perpendicular to the plane of the object’s rotation through the pointPabout which the object rotates is
called anaxis of rotation(seeFigure8.2).