PASCO ME-9341 INTRODUCTORY ROTATIONAL APPARATUS - Manual (Page 14)

10
Introductory Rotational Apparatus 012-03051F
F
d
⊥
➉ Turn the platter over. Go back to step 4. Use the smallest spindle and 0.4 newton of force.
Place the auxiliary platter on top of the main platter, and repeat the experiment. If you have
additional platters, repeat again using two or three platters on top of the main platter. Now
repeat the experiment first with the ring and then the steel bar on top of the main platter.
Analysis
Draw a graph of angular acceleration versus the step pulley
radius, given a constant applied force. Draw a second graph
of angular acceleration versus the applied force for a constant
step pulley radius. The angular acceleration of an object (a)
depends upon the torque (
τ
) applied to it and the moment of
inertia (I) of the object: a =
τ
/I. Torque equals the applied
force times the perpendicular distance from the axis of
rotation to the point of application of the force,
τ
= d
⊥
F (see
Figure 1.2).
In step 8 of the procedure, the applied force remained constant while the distance d
⊥
was
changed (d
⊥
is the step pulley radius). In your first graph, you should see that the angular
acceleration is directly proportional to d
⊥
.
In step 9 of the procedure, d
⊥
remained constant while the applied force was changed. There-
fore, your second graph should show that angular acceleration is directly proportional to the
applied force.
Finally, the angular acceleration is inversely proportional to the moment of inertia, given a
constant torque. The moment of inertia of an object depends on its mass and on how that mass
is distributed. In the first part of step 10, you increased the mass but kept the distribution the
same. What affect did the increased mass have on the acceleration? What affect did it have on
the moment of inertia?
The auxiliary platter, the ring, and the bar have approximately the same mass. Based on your
acceleration data, rank them from greatest to least in terms of their moments of inertia. Be
prepared to explain your logic for ranking them as you did in your Discussion. Do your results
agree with theory?
Report
Your report should include PURPOSE, PROCEDURE, DATA, and DISCUSSION. Your
discussion should include your Analysis. Compare rotational dynamics with linear dynamics
in your discussion.
τ
= d
⊥
F
Figure 1.2 The Geometry of Torque
Description of Applied Force Step Pulley Radius Angular Acceleration
Rotating Object (F) (d
⊥
) (
α
)
Table 1.1 Data
Name: Date: Group:
α = τ/Ι