School of Architectural, Civil and Mechanical Engineering
Dynamics. Experimental project: Moment of Inertia
PREAMBLE
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This experimental activity is designed to be undertaken in groups.
Each group, with equal contribution from each member, is to submit a comprehensive report
before 5.00 pm on the specified due date. Marks will be distributed equally between both
students.
Rules of the Mechanics laboratory (Room D328, TO in charge: L. Kovacs Room D328G) must
be followed:
o Authorisation from the technical officer in charge must be obtained before using the
equipment.
o Safety equipment must be worn and safety procedures followed when operating the
cam analysis machine.
o The safety guard must be in position when the motor of the cam analysis machine is
switched on.
o Any malfunction or equipment failure must be immediately reported to the technical
officer in charge
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1
INTRODUCTION
This experimental project is aimed at applying analytical and experimental techniques to develop an
understanding of moments of inertia. The moment of inertia of two wheel and axle units, one flywheel
and a connecting rod will be estimated using various experimental methods.
2
EQUIPMENT
The exercise will be based on three experimental rigs:
 An inclined plate
 Knife-edge pendulum supports
 A geared flywheel
The following instruments are provided:
 Digital weighing scales.
 A steel rule
 A stop watch
 A set of vernier callipers
3
3.1
PROCEDURE: WHEEL AND AXLE
Pendulum method
Develop an equation for the moment of inertia of each wheel
and axle about their central axis ‘O’ resting on the knife-edge
support with a pendulum attached as shown below. (Neglect
the mass of the pendulum bar and the effects of the grooves
in the axles). Hints: Use the parallel axis theorem; assume
small oscillations (sin = ).
Based on that equation, experimentally determine the
moment of inertia of each wheel and axle by attaching the
pendulum to each axle, and carefully measuring the
following:
 The mass of each wheel and axle
 The mass of the pendulum bob
 The length of the pendulum
 The radius of the axle
 The period of oscillation for small oscillations
School of Architectural, Civil and Mechanical Engineering
Dynamics. Experimental project: Moment of Inertia
3.2
Inclined plane method
Using the work-energy method, develop an equation for the moment of inertia of each wheel and axle
about their central axis when rolling between two points down an inclined plane. Hints: Ignore
frictional losses; the only force acting on the system is gravity (constant acceleration).
Based on that equation, experimentally determine the moment of inertia of each wheel and axle by
allowing each axle to roll down the inclined plane and carefully measuring the following:
 The rolling distance travelled
 The vertical distance travelled
 The mass of each wheel and axle
 The average time of travel
3.3
The geometrical calculation method
Estimate the moment of inertia of each wheel and axle about their central axis by carefully measuring
the mass and dimensions of each wheel and axle.
4
4.1
PROCEDURE: FLYWHEEL
Falling weight method
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Measure the flywheel diameter.
Measure the mass of the bob.
Wrap the cotton string around the flywheel rim and attach the bob.
Adjust the string length so that it automatically detaches from the flywheel rim as the bob
touches the ground.
Estimate the falling distance of the bob by turning the flywheel backward.
Release the flywheel and record the time taken for the mass to reach the ground
Record the total number of revolutions undergone by the flywheel between the time the
bob hit the ground and the flywheel came to a complete stop.
Using the work-energy method, develop an equation for the moment of inertia of the flywheel about its
central axis as a function of time of travel (bob) and number of flywheel rotations during deceleration.
Ignore any frictional losses. Hint: This is a constant acceleration situation.
5
5.1
PROCEDURE: CONNECTING ROD
Compound pendulum method
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Measure the mass of the connecting rod
Suspend the rod by one end on the knife edge and
record the average period of oscillations for small
oscillations
Suspend the rod by the other end on the knife edge and
record the average period of oscillations for small
oscillations
Measure the distance between the two support points.
Develop an equation for the moment of inertia of the connecting rod
about its centre of mass as a function of the periods of oscillation
measured. Hints: for small oscillations (sin = ); use the parallel
axis theorem.