Experiment 9

Rotation and Moment of Inertia

Objectives

To show that torque is directly proportional to angular acceleration.

Introduction

Torque is the rotational equivalent of force in the sense that angular acceleration is proportional to torque.

The proportionality constant is the moment of inertia of the rotating body rather than the mass of the

body (as is the case with force produced accelerations). Hence, a graph of torque vs. angular acceleration

should be a straight line with a slope equal to the moment of inertia of the body under consideration.

Procedure 1

Obtain an apparatus, timer, strings, and weights. Measure the radius of the wooden drum. Arrange the

pulley so that the string is wrapped around the drum on the axle runs horizontally over the pulley and

down. Set a small mass on the string and hang it over the pulley so that the apparatus rotates as the

weight falls. Study the apparatus from rest and let the weight fall a predetermined distance to the floor,

timing its fall. Repeat several times.

Rewind the string and put 20g on it. Release the wheel and record the times the weight requires for

falling the same predetermined distance as before. Repeat using 30, 40, 50 and 60g.

Procedure 2

Weigh the large washers provided and place them on the horizontal rod of the apparatus. Put the same

number on each side and snug them outward against the retaining pins. Measure their distances from the

axis. Now repeat Procedure 1.

Evaluation

Plot graphs of  τ  vs. α for both procedures. These quantities may be calculated from the equations

where m is the hanging mass, r is the radius of the wooden drum, s is the distance m is allowed to fall, and

t is the time of the fall. Obtain a least squares fit to each set of data. The slope of the line in each case is

the moment of inertia of the system. The difference of the slopes is the moment of inertia of the added

washers. Compare this value to that obtained from a calculation using the parallel axis theorem

where m the mass of all the washers and L is the distance from the axis to the center of mass of the

washers on each side (L is best measured for both sides and averaged). I_cm turns out to be about 0.1% of

mL² so we may neglect it and write for the moment of inertia of all the washers

I = mL²