Measuring the Moment of Inertia of a Flywheel

Measuring the Moment of Inertia of a Flywheel

Objective

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Measure the angular velocity of a flywheel and use conservation of

energy to calculate its moment of inertia.

Apparatus

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Flywheel

String

Slotted mass on hanger

Stop-watch

Vernier caliper

Metre ruler

Theory

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The rotational kinetic energy can be defined by the equation K=1/2 I ω2.

Where I is the moment of inertia of the body about the axis of

rotation.

In this experiment, the flywheel rotates freely about a horizontal

axis. The radius of the axle of the flywheel can be measured with a

caliper. As m falls, its gravitational potential energy is transferred

into translational kinetic energy of m, rotational kinetic energy of

the flywheel and work done by friction. As the flywheel completes N

further turns, its original rotational kinetic energy is transferred

into friction loss. Assume the flywheel decelerates uniformly. Thus,

the moment of inertia of the flywheel can be determined.

Procedure

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1. The flywheel was set as shown with the axle of the flywheel

horizontal. A polystyrene tile was placed on the floor to avoid the

impact of the mass on the floor.

2. The vernier caliper was used to measure the diameter d of the axle.

The mean of two perpendicular measurements was taken.

3. The hanger with appropriate amount of slotted mass was put on the

tile. Use the balance to measure the total mass m.

4. Sufficient length of string was attached to the hanger so that the

free end wraps once round the axle of the flywheel.

5. The mass was winded up to an appropriate height.

6. Verified that the string fell off the axle when the mass hit the

ground. A label was put on the curved surface of the flywheel. The

mass was winded up again.

7. The height h of the mass was measured. The height h was recorded.

The number of revolutions n1 that the flywheel made was calculated as