AN EXPERIMENT ON MOMENT OF INERTIA OF A DISC IN MOTION

ANEXPERIMENT ON MOMENT OF INERTIA OF A DISC IN MOTION

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ANEXPERIMENT ON MOMENT OF INERTIA OF A DISC IN MOTION

Objective:To determine the Moment of Inertia of a discin motion

The experiment entailed thefollowing equipment:

  • Moment of Inertia apparatus

  • Thread

  • Small masses

  • Digital Timer

  • Meter sticks

  • Vernier Calipers

Theory: When subjected to an external force, a stationary object tends tooppose or resist linear acceleration. Thus, the measurement of anobject resisting angular acceleration when subjected to externaltorque is known as moment of inertia, and it can be known as arotational analogue of mass. The moment of inertia denoted as of any object is influenced by three factors which include thesetting of the axis of rotation, the total mass the distribution ofmass relative to the axis of rotation. When mass mdescends the gravitational energy (potential energy),mgh,stored in mass mis transformed to the kinetic energy and part of the energy is thelinear kinetic energy denoted as ,and rotational kinetic energy denoted as exist in the disc apparatus.

Fromthe equation of energy conservation,

………………………………………………… (i)

Themoment of inertia can be formed by making the subject of the formula to be as in equationii.

………………………………………….(ii)

To get the measurement of I,there has to be a measurement of values of m, h, v, and ω.

Moment of inertia is related toinstantaneous velocity can be found by getting the average velocityof mass m attachedto a thread falling from a steady state. Equation(iii) gives theaverage velocity of the falling mass m.When releasing mass mto fall, the time interval forthe mass to fall is measured and from there once can get the averagevelocity which is given by

…………………………………… (iii)

However, the formulaneccessitates the use of the instantaneous velocityv, not the averagevelocity. The average velocity is different between two differentvelocities of the falling objects divided by two. Initial velocity iszero as it falls from still position,

Thus, ………… (iv).

Therefore making the subject of the formula results to and substitute the from the equation (iii),

…………………………………………………………………….(v)

When rotation an object, it hassame radius at all points of rotation to give rise to linear velocitygiven by …………………………………………………….(vi)

When rotating a smaller discattached by a thread, with reference point on the rim of the disc thelinear velocity is equal to that of a falling mass m, therefore,

Linearvelocity = angular velocity

,substituting the average linear velocity, therefore angular velocity

………………………(vii)

Having all the required detailsand equations, from equation (ii) and (vii)

Moment of inertia = ……………………………………..(ii)

Angular velocity ………………………(vii)

Substituting the angular velocityin equation (ii).

Moment of inertia =

Whereby Moment of inertia =

Mass, Radius, Height, Gravitation force, Time

Driving Mass &nbsp

&nbspTime Intervals

Final Velocity &nbsp

Moment of Inertia

0.050 &nbsp &nbsp &nbsp &nbsp &nbsp &nbsp &nbsp

9.88

0.377

0.468

0.100

7.12

0.524

0.484

0.150

5.76

0.647

0.473

0.200

4.91

0.759

0.457

0.250

3.52

1.059

0.289

Height (m)

Radius (m)

Average moment

1.864

0.366

0.434