For procedures, see your mechanical laboratory manual.

Title: Flywheels and Falling Weight


Aim

To determine the moment of inertia of a flywheel and to use this to verify newton's laws as applied in this case.

Theory

The flywheel consists of a heavy circular disc/massive wheel fitted with a strong axle projecting on either side. The axle is mounted on ball bearings on two fixed supports. There is a small peg on the axle. One end of a cord is loosely looped around the peg and its other end carries the weight-hanger.

unction is to minimize the speed fluctuations which occur during the working of machines. The Flywheel acquires kinetic energy from the machines. The capacity of storing KE (kinetic energy) depends on the rotational inertia of the flywheel. This rotational inertia is called as Moment of Inertia of rotating objects namely wheels.

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


In this experiment, the flywheel rotates freely about a horizontal axis. The radius of the axis 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, the 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 the SI system of units, the unit of moment of inertia is Kg.m2 (kilogram meter square)


Let "m" be the mass of the weight hanger and hanging rings (weight assembly). When the mass "m" descends through a height "h", the loss in potential energy is
The resulting gain of kinetic energy in the rotating flywheel assembly (flywheel and axle) is
Where
I -the moment of inertia of the flywheel assembly
ω - angular velocity at the instant the weight assembly touches the ground.

The gain of kinetic energy in the descending weight assembly is,
Where v is the velocity at the instant the weight assembly touches the ground. 

The work done in overcoming the friction of the bearings supporting the flywheel assembly is
Where
n - number of times the cord is wrapped around the axle
Wf - work done to overcome the frictional torque in rotating the flywheel assembly completely once
Therefore from the law of conservation of energy we get
On substituting the values we get
Now the kinetic energy of the flywheel assembly is expended in rotating N times against the same frictional torque. Therefore
and
If r is the radius of the axle, then velocity v of the weight assembly is related to r by the equation
Substituting the values of v and Wf we get:
Now solving the above equation for I


Applications

Flywheels can be used to store energy and used to produce very high electric power pulses for experiments, where drawing the power from the public electric network would produce unacceptable spikes. A small motor can accelerate the flywheel between the pulses.

The phenomenon of precession has to be considered when using flywheels in moving vehicles. However, in one modern application, a momentum wheel is a type of flywheel useful in satellite pointing operations, in which the flywheels are used to point the satellite's instruments in the correct directions without the use of thrusters rockets.

Flywheels are used in punching machines and riveting machines. For internal combustion engine applications, the flywheel is a heavy wheel mounted on the crankshaft. The main function of a flywheel is to maintain a near-constant angular velocity of the crankshaft.

References

  1. Inertia, wikipedia.org.
  2. Moment of Inertia, wikipedia.org.
  3. Moment of Inertia of Flywheel, Advanced mechanics virtual lab, Physical sciences, Amrita Vishwa Vidyapeetham University.
  4. Moment Of Inertia Of Flywheel, IIT JEE Study Material, byjus.com.
  5. Moment Of Inertia Of A Flywheel By Falling Weight Method, oureducation.com.