Updated: Dec 23rd, 2025

Newton’s Second Law and Torque: Angular Acceleration Experiment Report

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Table of Contents

Introduction
Data
Results
Conclusion
Reference

Introduction

The present laboratory work is based on Newton’s second law of motion, which postulates the relation between the applied force and the acceleration for a body, F = ma (OpenStax, 2022). An experiment was performed to change the values of a suspended weight, stimulating the rotor motion to evaluate the patterns of such rotation. Increasing the mass of the suspended weight caused the device to spin faster, and assessing the nature of this relationship was at the heart of this lab work. Since neither torque nor angular acceleration could be measured directly, indirect calculations of these values were performed.

Data

Table 1 shows the results of the direct measurements obtained during the experiment, as well as the results of indirect measurements of acceleration, angular acceleration, and torque. The angular acceleration could not be measured directly, so it was calculated using Equation [1] with the shaft radius in mind. Torque also could not be measured directly and was calculated for Equation [2].

Table 1. Results of primary measurements and indirect calculations of acceleration, angular acceleration, and torque

Mass, kg.	Time, sec.	Acceleration, m/s²	Ang. Acceleration, s^-2	Torque
0.100	36.91	0.00151797	0.237182406	0.006272
0.150	27.54	0.00272661	0.426032459	0.009408
0.200	23.67	0.00369109	0.576731994	0.012544
0.250	21.56	0.00444890	0.695141229	0.01568
0.300	20.00	0.00517000	0.8078125	0.018816
0.350	18.25	0.00620905	0.970163258	0.021952
0.400	16.73	0.00738854	1.154459438	0.025088

Results

Calculations

For the first measurement, an example of angular acceleration calculations is shown in Equation [1], but the process was the same for all tests. An example of torque calculations for the first measurement is provided in Equation [2], but the process was the same for every test.

Graphs

Figure 1 shows the dependence of torque on the angular acceleration of the device, with the regression line plotted. As can be seen, the relationship between the two variables is well described by the ascending straight line with a coefficient of determination of 0.997, which corresponds to the coverage of 99.7% of the variance of the data.

Figure 1. Dependence of applied torque on angular acceleration.

The slope of this straight line is 0.0214 N.s², which means that for every one-unit increase in angular acceleration, the applied torque increases by 0.0214 N.m. The y-intercept value makes no physical sense because it is responsible for a non-zero torque at zero angular acceleration. Similarly, the reverse is also true; when the torque was zero, the x-intercept was -0.0360 m.s^-2, which also made no physical sense.

Conclusion

The present laboratory work was constructed to test Newton’s second law of motion with respect to the torque device. Changing the values of the weight that makes the rotor come into motion influences the angular acceleration and, therefore, makes the device rotate faster. The calculations and statistical analysis showed an upward linear relationship between the applied torque and angular acceleration. This means that an increase in one variable leads to an increase in the other.

These data agree well with theoretical expectations since Newton’s second law of motion indicates a direct relationship between force (torque) and acceleration (angular acceleration). With some assumptions due to measurement errors and uncertainties, the result obtained perfectly satisfies the physical principle.

Reference

OpenStax. (2022). Newton’s second law of motion: Concept of a system. OpenStax. Web.