Measuring the moment of inertia of a flywheel.

Precautions

1. The mass and the height from which the mass falls should be chosen so that the falling time is long enough for measurement to be taken accurately. The mass and the height should not be changed throughout the experiment once they have been chosen.
2. The first few turns of the string should overlap the others.
3. The mass should be wound up to the same height in all trials.
4. When using the stop-watch, the hand should be held straightly to minimum the reaction time error.
5. Do not stand too close to the polystyrene tile when releasing the mass.
6. When choosing the appropriate amount of the slotted mass, a smaller amount (e.g. 1 slotted mass) should be chose to try first.
7. The later turns of the string should not overlap the others.

Result and calculation

Mass m                        = 0.2 kg

Height h                        = 0.80 m

Axle diameter d        = 0.0522 m

→ radius r                = 0.0261 m

Suppose v is the final velocity of the mass when it reaches the floor and ω is the angular velocity of the flywheel at this instant. Then

v = 2 × average velocity during fall = 2h / t

= 2 × 0.8 ÷ 1.81

= 0.88 m s-1

ω = v / r

= 0.88 ÷ 0.0261

= 33.9 rad s-1

From the conservation of energy,

Decrease in                                        Increase in                                        Work done

gravitational potential        =                kinetic energy                        +                against

energy of falling mass                        of mass and flywheel                        friction

i.e. mgh = 1/2 mv2 + 1/2 Iω2 + n1W

where W is the work done against friction per revolution.

Since the kinetic energy acquired by the flywheel ( 1/2 Iω2) is dissipated in n2 revolutions,

n2W = 1/2 Iω2

W = Iω2 / 2n2

Substituting,

mgh = 1/2 mv2 + 1/2 Iω2 + n1W

mgh = 1/2 mv2 + 1/2 Iω2 + n1Iω2 / 2n2

I = mr2 ( n2 / n1 + n2 ) ( gt2 / 2h – 1)

 =0.2 × (0.0261)2 ( 25 / (25 + 5) ) ( 10 × (1.81)2 / 2 × 0.8 – 1 )

 =2.21 × 10-3 kg m2

Conclusion

The moment of inertia of the flywheel is measured and found to be 2.21 × 10-3 kg m2.

Discussion

Errors and improvement

1. The reaction times error. This can be improved by straighten the hand when taking the time.
2. The number of revolution n2 that the flywheel performed cannot be accurately obtained. This can be improved by counting the number of revolution by two students instant of one and to repeat the experiment more times.
3. Unsteady hands. When the hand released the mass, force may be push to the mass. To improve this, student should release the mass slowly and softly.

Reference

Physic Beyond 2000