# Moment of Inertia of a flywheel by falling weight method

**moment of inertia of a flywheel**

**EXPERIMENT : To determine the moment of inertia (MOI) of flywheel by falling weight method**

**Apparatus Required:**

1. Flywheel 2. String 3. Stop-watch

4.Vernier caliper 5. Meter ruler 6. Slotted mass on hanger

**THEORY : **

Flywheel is a solid disc mounted on the shaft of machines such as turbines, steam engines, diesel engines etc. When the load of such machines suddenly increases or decreases its function is to minimize the speed fluctuations which occurs during the working of machines.The Flywheel acquires kinetic energy from the machines.The capacity of storing of KE (kinetic energy) depend on the rotational inertia of the flywheel.This rotational inertia is called as Moment of Inertia of rotating object namely wheels.

The **moment of inertia** of body is defined as the measure of object’s resistance to the changes of its rotation.

In this experiment, the flywheel rotates freely about a horizontal axis. The radius of the axie of the flywheel can be measured with a caliper. As ( m ) falls, its gravitational potential energy (PE) 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.

For the known mass density & geometry of the material used, in SI system of units the unit of moment of inertia is Kg.m2 (kilogram meter square)

**Procedure to perform the Experiment : **

1. The flywheel is set 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 is 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 is put on the tile. Which is used the balance to measure the total mass m.

4. The mass is winded to an appropriate height. Verified that the string fell off the axle when the mass hit the ground.*
*5. The height h of the mass is measured. The height h was recorded.

6. The mass is released then and at the same time the stop-watch is started.

7. As soon as the mass hit the ground, timing was stopped and the number of revolution the wheel revolved is taken.

8. The mass is winded up again and steps are repeated for at least 3 times.The mean time of the falling is obtained.

**PRECAUTIONS :**

1. Do not stand too close to the polystyrene tile when releasing the mass.

2. The turns of the string must not overlap the other.

3. Stop Watch must be handled with care in order to avoid any error in the reading.

4. The first few turns of the string should overlap the others.

5. The mass should be wound up to the same height in all trials.

**Some Important questions and answers related to the Experiment: **

**Q:** What do you understand by MOI ?

**Ans**: MOI stands for moment of inertia.It is a quantity expressing body’s tendency to resists angular acceleration.

**Q:** Give the expression for the MOI of Flywheel.

**Ans**: mgh = ½ mv^{2} + ½ Iω^{2} + n_{1}E

**Q:** Draw the labelled diagram of Flywheel setup for calculation of MOI ?

**Ans**:

**Q:** List the apparatus required in the experiment ?

**Ans**: 1. vernier caliper

2. Flywheel

3. string

4. meter ruler

5. Stop watch

6. slotted mass on hanger.

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