2. Flywheel

University: Jamia Millia Islamia

Course: Lab I (PHB11L)

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Experiment-2

Moment of inertia of a fly-wheel

Object:

To determine the moment of inertia of a fly-wheel about its axis of rotation.

Apparatus:

The flywheel, weight box, thread, stop-watch, meter scale and vernier callipers.

Theory:

A fly wheel is a heavy wheel free to rotate about its axis. It generally has a large moment of inertia. When

it rotates with an angular velocity ω, the energy due to rotation, called rotational kinetic energy is given

by

W=1

2Iω2(1)

Figure 1: The Flywheel Setup

In the given experiment, a wheel is set into motion by winding a

string around the axle of the wheel, and attaching a mass m, at

the end of the string. As the weight falls, the string unwinds, first

slowly, and then faster and faster. The potential energy of the

weight as it lowers, thus gets converted into the rotational kinetic

energy of the wheel and the kinetic energy of the wheel itself. If

we choose the length of the string such that before the weight

reaches the ground, the weight falls, then we know that energy

conservation requires

mgh = rotation K.E. of wheel at the time when the string

detaches itself

+ linear kinetic energy of the mass m

+ energy lost due to friction

i.e.

mgh =1

2Iω2+1

2mv2+Efriction (2)

h= the height which the weight covers between the time the string begins to unwind and the time when

the string det aches itself from the axle

The case when friction is small

If there is negligible friction, then

mgh =1

2Iω2+1

2mv2(3)

Where ωis the angular velocity of the wheel at the time when the string leaves the wheel, and vis the

downward speed of mat that time. From this equation we can find Ias follows. If there is no friction,

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