3B Scientific Rotation Apparatus - Manual (Page 2)

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Subject to technical amendments
© Copyright 2012 3B Scientific GmbH
3. Technical data
Crossbar: 600 mm x 8 mm diam.
Groove separation: 40 mm
Weights: 2x 50 g, 2x 100 g,
2x200g
Diameters of multiple
pulley: 30 mm, 45 mm,
60 mm, 75 mm
Overall weight: 7 kg
4. Additionally required
1 Ruler, 1 m 1000742
2 Mechanical stopwatches, 15 min 1003369
5. Sample experiments
5.1 Calculating angular acceleration
• Place masses on crossbar and secure with
screws, insert thread and wind around mul-
tiple pulley, run thread over pulley and wind
up, connect to mass hanger keep threat per-
pendicular 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 ta-
kes 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 cross-
bar in radians/second, remembering that
one rotation is 2 π radians.
• Angular acceleration is given by the equation
t
Δ
ω Δ
= α
• 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.
• Change hanger mass, mass on the rod and
position of the mass on rod and casually
compare effects on angular velocity.
5.2 Calculating torque M
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:
θ ⋅ ⋅ = sin F r M
90 = θ because the thread is perpendicular to
the radius of the apparatus. r is the radius of the
multiple pulley
g m F
⋅ = where m is the sum of
the slotted masses and hanger and
2
81 , 9
s
m
g
= ,
the gravitational acceleration constant. Thus, the
theoretical torque is given by:
g m r M
⋅ ⋅ =
• To find experimental torque, first calculate
the angular acceleration using the methods
outlined in section 5.1.
• Calculate the moment of inertia J by meas-
uring the distances to the masses on the
crossbar and using the following equation
2 2
12
1
R M L M J
weights rod
+ =
M
rod
= weight of crossbar
L = length of crossbar
M
weights
= weight of masses on crossbar
R = distance mass on crossbar - axle
• Multiply angular acceleration by the moment
of inertia to find torque
α ⋅ = J
M
• 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 J
• 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:
α
=
M
J
• Repeat the experiment, keeping the mass
on the crossbar fixed and varying the dis-
tance.
• Plot moment of inertia versus distance.
• Repeat the experiment, but this time keep
the distance fixed and vary the mass on the
rod and plot moment of inertia versus mass.
You should find that the moment of inertia varies
accoring to the equation
2
R M J
⋅ =