To find the moment of inertia of a flywheel

 To find the moment of inertia of a flywheel.

 

Apparatus: 

A flywheel, a few different masses, and a mass provided with a hook, a strong and thin string, stopwatch, a meter rod, vernier callipers, and marker.

 

Theory:

A flywheel is a solid disc of significant size and weight with a long axle. Its function is to minimize speed fluctuations that occur when the load on the machine is suddenly reduced or increased. The flywheel derives excess kinetic energy from the engine when the load on the engine is less or running at idle and supplies stored energy to the engine when subjected to a greater load. The storage/release capacity of kinetic energy depends on the rotational inertia of the flywheel. This inertia of rotation is known as the moment of inertia of the flywheel. 

 

   Moment of inertia of the flywheel is given by 

 

                        

 

 

Where m = mass which allows falling

h = height through which the mass is fall

 ω = angular velocity = 4 π n_2/t

t = time to make  n₂  revolution.

n₁ = No. Of revolutions, the wheel makes during the decent of mass

n₂= No. Of revolutions made by wheel after the string detached from the axle

 

Procedure:

1. Examine the wheel and see that there is the least possible friction. Oil the bearings if necessary.

2. Measure the diameter of the axle with vernier callipers at different points and find the mean Measure also the circumference of the wheel W with a thread. 

3. Take a strong and thin string whose length is less than the height of the axle from the floor. Make a loop at one end and slip it on a pin on the axle. Tie a suitable mass to the other end of the string. Suspend the mass by means of the string so that the loop is just on the point of slipping. Make a mark on the wheel behind the pointer in this position. Also, note the position of the lower surface of the mass m on a scale fixed behind the wall.

4. Now rotate the wheel and wrap the string uniformly around the axle so that the mass m is slightly below the rim of the wheel. Note the position of the lower surface of the mass on the scale.

5. Now allow the string to unwind releasing the mass. Count the number of rotations of the flywheel h when the mass touches the ground.

6. Switch on the stopwatch when the moment the mass touches the ground and again count the number of rotations of the flywheel, n₂ before it comes to rest. Stop the watch when the rotation ceases and note down the reading t.

7. Repeat the measurement at least three times with the same string and mass such that n_1, n₂   and t are closely comparable. Take their average value.

8. Repeat the experiment for another mass. 

 

Observations:

 

Vernier constant=..............

 

Diameter of the axle D₁=...................

                                  D₂=....................

                                  D₃=..................   

Mean diameter of the axle D = D₁+D₂+D₃  = ................

 

The radius of axel r = D/2 = ...............

 

Observation Table:

S.No.	Mass (in g)	No. of Revolution  n1			No. of Revolution n2			Time (t)
		Reading 1	Reading 2	Mean n1	Reading 1	Reading 2	Mean n2	Reading 1	Reading 2	Mean (t)
1.	100
2.	150
3.	200

 

 

 

Result: 

Movement of inertia of a fly wheel = __________ Kg m² 

 

Precautions: 

I. There should be the least possible friction in the flywheel. So that the flywheel starts of its own accord and no push is imparted to it. The mass tied to the end of the cord should be of such a value that it is able to overcome friction at the bearings and thus automatically starts falling. 

2. The length of the string should be less than the height of the axle of the flywheel from the floor.

3. The loop slipped over the pin should be loose enough to be detached easily.

4. The string should be thin and should be wound evenly.

5. The stopwatch should be started just when the string is detached. 

 

 

Source of error:

 (i) The angular velocity to has been calculated on the assumption that the friction remains constant when the angular velocity decreases from ɷ to zero. In actual practice, this is not the case because the friction increases as the velocity decrease. 

(ii) The instant at which the string is detached cannot be correctly found out.

 

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