**Experiment: Determination of moment of Inertia of a Fly Wheel**

**Theory:** Suppose, angular velocity of a wheel is ω and its radius r. Then lineal velocity of the wheel is, v = ωr. If the moment of inertia of a body is I and the wheel is rotating around an axle.

Then its rotational kinetic energy, **E = ½ Iω ^{2}.**

**Apparatus:** An iron axle, a heavy wheel, some ropes, a mass, stop watch, metre scale, slide callipers.

**Description of the apparatus:**

(1) First of all, let us measure the radius of the axle by a slide callipers.

(2) Then for the determination of number of rotation a mark by a chalk is put on the axle and a rope is wound on the axle. At the other end of the rope a mass m is fastened and if it is dropped from position R, the wheel after rotating a few times, the weight with the rope will fall to position S. The wheel makes m_{1} number of rotation to touch the point S and time for this drop is noted from the stop watch.

Now the rope is again wound on the axle and the mass is fastened on the other end of the rope. From position R the mass is allowed to fall to the ground and as soon as at touches the ground, the stop watch is started. When the axle comes to rest the stop wealth is stopped. Total time and number of rotation of the wheel before it comes to rest are noted i.e., total number of rotation (n_{2}) as noted.

**Table 1: radius (r) of the axle B**

**Table 2: Determination of time and number of rotation**

**Calculation**: If the axis takes time t for n_{2} number of rotation, then average angular velocity,

**ω _{2} = (2πn_{2})/t**

The axle acquires zero velocity with uniform retardation from angular velocity ω, so its average angular velocity,

ω_{2} = (ω + 0) / 2 = ω/2

or, (2πn_{2})/t = ω/2

or, **ω = 4πn _{2} rad S^{-1}**

Then, I = (2mgh – mω^{2}r^{2}) / ω^{2} (1+ n_{1}/ n_{2}) = ….. g.cm^{2} = ….. Kg.m^{2}

By inserting the value of n_{2}, ω can be found out. By increasing the values of m, ω, r, h, n_{1}, n_{2} and g in equation; moment of inertia of the heavy wheel can be found out.

**Precautions:**

(1) In the axle rope is to be wounded in such a way that while unwinding from the wheel it can easily drop on the ground.

(2) Number of rotation n and time t is to be unwired correctly.

(3) Height h is to be measured from the mark on the axle.

(4) h is to be measured correctly.