3B Scientific Rotation Apparatus User Manual

3B SCIENTIFIC

Rotary Motion Apparatus 1010084

Instruction sheet

11/12 ALF

®

PHYSICS

1 Base
2 Frame
3 Weight discs 50 g
4 Weight discs 200 g
5 Weight discs 100 g
6 Rotating axle

1. Safety instructions

To avoid injuries:

• Maintain a safe distance from the device
while it is in operation. Be especially careful
to keep your eyes and face away from mov­ing parts.

• Do not use your hand to spin the apparatus
to a high angular velocity! The screws are
not designed to stay in position at high ve­locities and the weights will fly off.

7 Multiple pulley
8 Crossbar
9 String
10 Hanger for slotted weights
11 Deflection pulley

2. Description

The rotary motion apparatus is used for investi­gating the effect of a constant torque on a rotat­ing body with variable moment of inertia.

A vertical, rotating axle on ball bearings in a
stable frame.supports a crossbar with equidis­tant grooves for holding the weights. For safety,
the weights are fixed in place with screws. The
torque is generated by a rotating plate with
hooks and up to three slotted weights, acting via
a string threaded over a multiple pulley with four
different pulley diameters.

1

3. Technical data

θ⋅⋅

=

=

θ

⋅

=

⋅⋅=

α⋅=

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 mul­tiple pulley, 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 stop­watches.

• 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 cross-
bar in radians/second, remembering that
one rotation is 2 π radians.

• Angular acceleration is given by the equation

ωΔ

=α

tΔ

• 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:

sinFrM

90

because the thread is perpendicular to

the radius of the apparatus. r is the radius of the

gmF

multiple pulley

the slotted masses and hanger and

where m is the sum of

m

81,9

g =

2

s

the gravitational acceleration constant. Thus, the
theoretical torque is given by:

gmrM

• 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

1

12

= weight of crossbar

M

rod

+=

weightsrod

22

RMLMJ

L = length of crossbar
M

= weight of masses on crossbar

weights

R = distance mass on crossbar - axle

• Multiply angular acceleration by the moment
of inertia to find torque

JM

• 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 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:

M

=

J

α

• Repeat the experiment, keeping the mass

on the crossbar fixed and varying the dis­tance.

• 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

RMJ ⋅=

,

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Subject to technical amendments

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