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2. Description
The rotational motion apparatus is used for de-
termining the angular acceleration as a function
of torque and for determining the moment of
inertia as a function of the distance of the body
from the axis and its mass.
A vertical, rotating axle with agate bearing sup-
ports a crossbar for holding the weights. The
force of the driving weight is transferred via a
pulley and a cord wrapped around a spindle on
the axis.
3. Technical data
Base plate:
Crossbar:
Spindle:
Weight:
4. Additionally required
Meter Stick
Digital Stopwatch
5. Sample experiments
5.1 Calculating angular acceleration
•
Place masses on crossbar and secure with
weight fasteners, insert thread and wind
around spindle, run thread over pulley and
wind up, connect to mass hanger keep
threat perpendicular to spindle. Hold mass
hanger.
•
Have two students standing ready with stop-
watches.
•
Release the mass hanger.
•
One student will record the time between
the release of the mass hanger and when it
touches the ground.
200 mm x 140 mm
600 mm
9/18 mm diam.
approx. 1.3 kg
1000742
1002811
•
As soon as the mass touches the ground,
the second student will record the time it
takes the crossbar to rotate twice. Be sure
to take this measurement before the appara-
tus has slowed due to friction.
•
Calculate angular velocity ω of the crossbar
in radians/second, remembering that one ro-
tation is 2π radians.
•
Angular acceleration is given by the equa-
tion
Δ
ω
α
=
t Δ
Δω is the value calculated for final angular
velocity (initial was zero) and Δt is the time it
took the mass to fall to the ground.
•
Repeat your measurement a few times and
average the results.
•
Repeat experiments by changing hanger
mass, mass on the rod and position of the
mass on rod and compare effects on angu-
lar velocity.
5.2 Calculating torque
The torque can be calculated theoretically and
experimentally and these two values can be
compared. Use the same experimental setup as
in 5.1.
The theoretical torque is given by the equation:
τ
=
=
sin
r
x
F
rF
θ
=
90
because the thread is perpendicular to
the radius of the apparatus. r is the radius of the
spindle. F = mg where m is the sum of the slot-
ted masses and hanger. Thus, the theoretical
torque is given by:
τ
=
⋅
⋅
r
m
g
•
To find experimental torque, first calculate
the angular acceleration using the methods
outlined in section 5.1.
•
Calculate the moment of inertia by measur-
ing the distances to the masses on the
crossbar and using the following equation
1
=
⋅
⋅
I
M
L
rod
12
•
Multiply angular acceleration by the moment
of inertia to find torque
τ I
=
⋅
α
•
Measure the change in torque from chang-
ing spindle radius and from varying the
amount of mass on the hangers.
5.3 Calculating moment of inertia
•
Measure the distance from the mass to the
pivot axle.
2
θ
2
2
+
⋅
M
R
weights
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