# Inertia lab report

Topics: Moment of inertia, Measurement, Mass Pages: 14 (935 words) Published: March 10, 2014
ES184 Mechanics, Structures and
Thermodynamics

Inertia Laboratory Report

Summary
The objective of this report is to find the Moment of Inertia of a disc by means of investigating the use of rotational motion. We then used the results of the experiments to plot a graph showing the relationship between the mass of the weight with the time taken by load to pass the distance of length of the string. Three different size discs were used in these experiments to determine the influence the size of a disc will have on its Moment of inertia. The outcome showed that the larger the radius and the mass of the disc, the larger the Moment of Inertia.

Introduction and theory.......................................................................................1 Method and observation.....................................................................................2 Results..................................................................................................................3 Calculations..........................................................................................................5 Error Analysis.......................................................................................................6 Graphical Representation....................................................................................7 Discussion and Conclusion...................................................................................9

Introduction and theory:

A laboratory experiment was carried out in order to find the Moment of Inertia of a disc by using rotational motion. The aim of the report was to analyze our findings and use our knowledge of physics to explain the results.

A Rotational motion experiment is the simplest method of finding the Moment of Inertia. Minimum equipment is required to perform this experiment. For the purposes of increasing the accuracy of the results, the procedure should be repeated three times, making our conclusion more reliable.

While load is moving downwards it’s potential energy converts to kinetic. Load is accelerating because weight(Fg=mg) of the load is bigger than tension on a string so load is not in equilibrium and by Newton’s Second Law (F=ma) resultant force creates an acceleration. Resultant force can be calculated by the equation S=0.5at2+ut to find acceleration and F=ma. String rotates the spindle which rotates the disc by creating a 𝒂

torque(T=Fr). Torque accelerates the disc and it can be found by α= 𝒓. To find moment of inertia now T=Iα equation is used.

1

Method and observation:
Apparatus: 3 different size discs, spindle, ruler, set of weights, stopwatch, stand. Disc is attached to one end of the spindle and string with load is attached to the other end. Disc’s weight, diameter and radius are required to be measured before experiment. Length of the string (L), number of loops on the spindle (n) and horizontal distance of loops (H) were measured before experiment. Using equation below r is found.

𝑟=

𝐿²−𝐻²
2𝜋𝑛

Spindle

Disc

String
Stopwatch
Weights
Stand

After setting all the equipment up the experiment starts. The string is then wrapped around the spindle. Time was measured for load pass the distance of length of the string. To plot graph one over time2 is required to be calculated. 4 different masses of the load are used in experiment is repeated 3 times every time mass is changed to make reduce random error. After finishing all the experiments on one of the discs other disc is placed and experiment repeats. When all the experiments are done and measurements are recorded mass against one over time2 is plotted using results. 3 graphs are going to be plotted for each disc. Gradient of the graph is constant k which we could use to find I using formulae below. When observed the string with vibrating and load was moving a little which can cause some systematic error. While spindle is spinning there is some friction...