Laboratory 8
Rotational Motion II: The Rotating Bar
Introduction
In Laboratory 6, we investigated moment of inertia and the ways in which it differs from mass.
We also looked at a situation (the inclined plane) in which both translational and rotational kinetic
energy come into play, and saw how rotational kinetic energy plays a role in twodimensional
inelastic collisions between extended objects. In this laboratory, we will expand our knowledge of
rotational dynamics to include the concept of
torque
, and we will examine energy conservation
in another context: a rotating bar. We will also use the rotating bar to explore the conservation of
angular momentum in two situations, one of which will lead directly into our analysis of gyroscopic
motion in the following laboratory.
Theoretical Background: Force vs. Torque
Simply put,
force
is something that can change the velocity of a body. Similarly,
torque
is some
thing that can change the
angular
velocity of a body. Even though forces are required to generate
torques, it is important to remember that torque is
not
a force. Torques and forces are both vectors,
so we have to deal with them using the tools of vector algebra.
The
magnitude
of a torque experienced by a rigid object about a particular axis of rotation can be
calculated using
τ
=
r F
sin
(
θ
)
,
(1)
where
τ
is the magnitude of the torque,
F
is the magnitude of the applied force, and
r
is the
magnitude of the vector
r
(also known as the
lever arm
) that points from the axis of rotation to the
point at which the force is applied. (For diagrams, see Figures 1 and 2.) In this equation, we also
have an angle
θ
, which is the angle subtended from
r
to
F
.
What does this equation tell us? First, it tells us that we can only calculate torque relative to a
particular axis of rotation  the torques an object experiences will differ depending on which axis
we choose, because the
r
in Equation 1 will change. Second, it tells us that a force is needed to
create a torque, but that not all forces create torques  a force can only create a torque if it is applied
at some nonzero distance from the axis of rotation. A similar force applied further from the axis
of rotation will generate more torque. An illustration of this idea is shown in Figure 1.
Problem 8.1
Why is it easier to open a door by pushing on the handle than
by pushing near the hinge?
65
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F
F
F
r
r
r = 0
90
90
Most Torque
Less Torque
No Torque
Figure 1:
Forces applied at different distances from a pivot.
Equation 1 also tells us that a force applied perpendicular to
r
will generate more torque than the
same force applied parallel to
r
. Hint: What is
sin
(
0
)
? See Figure 2.
F
r
90
Most Torque
Less Torque
No Torque
F
r
45
F
r
Figure 2:
Forces applied at different angles.
Problem 8.2
Give a physical/geometric interpretation of
F
sin
(
θ
)
. What
does this term represent?
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 Spring '11
 Gerson
 Angular Momentum, Moment Of Inertia, Ibar, Law of Conservation of Angular Momentum

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