Determine the moment of inertia of a flywheel.

Experiment to determine the moment of inertia of a flywheel using falling weights, measuring the axle, rotations, and time to calculate rotational inertia.

Apparatus

• Flywheel

• Two weights: 300 g and 200 g

• Cotton string

• Stopwatch

• Metre rod

• Vernier caliper

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Observations

• Vernier constant of caliper: … cm

• Diameter of axle (1st position, d₁): … cm

• Diameter of axle (2nd position, d₂): … cm

• Mean diameter of axle: d = (d₁ + d₂)/2 = … cm

• Radius of axle: r = d/2 = … cm

Procedure

1. Make a small loop at one end of the string and place it around the peg P on the flywheel axle. Tie a weight (Mg) at the other end.

2. Rotate the wheel by hand to wind the string around the axle. When the weight is slightly below the rim (point A), mark this position on the wall using a set square.

3. Let the weight descend while the string unwraps as the wheel rotates. Adjust the string length so that when the weight rests on a wooden block W, the string is just tight on the peg. Mark this position as B on the wall.

4. Count the number of rotations (m) the wheel makes as the weight falls from A to B. Observe the mark on the rim for accuracy.

5. Rewind the string so the weight is at A, remove the block, and let the weight fall. Start the stopwatch as soon as the weight detaches from the peg. Count the number of rotations (n) until the wheel comes to rest and record the time.

6. Measure the axle diameter in two perpendicular directions and calculate the mean radius.

7. Repeat the experiment using a 300 g weight and then a 200 g weight in the hanger.

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Calculations

• Use the formula for moment of inertia:

$$I=\text{(formula based on rotations, time, and dimensions)}$$

• Moment of inertia of the flywheel about its axle: I = … gm·cm²

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Precautions

1. Mark the bottom positions of the weight on the wall for both A and B positions.

2. Measure the axle diameter in two perpendicular directions.

3. Adjust the string length so that it is tight and just about to slip from the peg when the weight rests on the block.

4. Start timing and counting rotations immediately as the weight detaches from the peg.

5. If the wheel makes fewer than 100 rotations before stopping, check for excessive friction and oil the axle.

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Viva-Voce

Q1. What is meant by moment of inertia?
A: The resistance of a rotating body to change its state of rotation or rest.

Q2. What is the radius of gyration?
A: The radius of a thin ring centered on the axis, having the same mass and moment of inertia as the body.

Q3. Does moment of inertia depend on the axis of rotation?
A: Yes, it depends on the axis of rotation.

Q4. What is meant by inertia?
A: Inertia is a property of a body to continue its motion unless acted upon by a force. It depends on the mass of the body.

Q5. Where is the center of gravity of the flywheel?
A: It lies on the axis of rotation.

Q6. Give the units of moment of inertia.
A: gm·cm² or kg·m²