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Idiomas disponibles
Idiomas disponibles
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.
•
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 apparatus has slowed
due to friction.
•
Calculate angular velocity, ω, of the crossbar in
radians/second, remembering that one rota-
tion is 2π radians.
•
Angular acceleration is given by the equation
∆
ω
α
=
t ∆
∆ω is the value calculated for final angular ve-
locity (initial was zero) and ∆t is the time it
took the mass to fall to the ground.
Elwe Didactic GmbH ▪ Steinfelsstr. 6 ▪ 08248 Klingenthal ▪ Germany ▪
3B Scientific GmbH ▪ Rudorffweg 8 ▪ 21031 Hamburg ▪ Germany ▪
200 mm x 140 mm
600 mm
9/18 mm Ø
approx. 1.3 kg
8401550
U11902
Subject to technical amendments
•
Repeat your measurement a few times and
average the results.
•
Try changing hanger mass, mass on the rod
and position of the mass on rod and casually
compare effects on angular velocity.
5.2 Calculating torque
The torque can be calculated theoretically and
experimentally and these two values can be com-
pared. Use the same experimental setup as in 5.1.
The theoretical torque is given by the equation:
τ
=
=
θ
r
F x
rF
sin
θ
=
90
because the thread is perpendicular to the
radius of the apparatus. r is the radius of the spin-
dle. F=mg where m is the sum of the slotted
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 out-
lined in section 5.1.
•
Calculate the moment of inertia by measuring
the distances to the masses on the crossbar
and using the following equation
1
=
+
2
I
M
L
M
rod
weights
12
•
Multiply angular acceleration by the moment
of inertia to find torque
τ I
=
α ⋅
•
Measure the change in torque from changing
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.
•
Calculate the angular acceleration as in 5.1
•
Calculate the theoretical torque as in 5.2
•
The moment of inertia is given by the equa-
tion:
τ
=
I
α
•
Repeat the experiment, keeping the mass on
the crossbar fixed and varying the distance.
•
Plot inertia versus distance.
•
Repeat the experiment, but this time keep the
distance fixed and vary the mass on the rod
and plot inertia versus mass.
You should find that the moment of inertia varies
accoring to the equation
I =
2
MR
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