The aim of this experiment is to use experimental data for a rotating system accelerated from rest to build graphical and mathematical models for the system

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Forces on a rotating system
Purpose
The aim of this experiment is to use experimental data for a rotating system accelerated from rest to
build graphical and mathematical models for the system.
Equipment
1. Computer
2. Electronic or triple beam balance
3. Mass hanger
4. Metal cylinders (2)
5. Meter stick
6. Rotational motion apparatus
7. Scissors
8. Slotted masses
9. Stopwatch
10. String
11. Threaded rod
12. Wing nuts (4)
Introduction
The figure below shows the various parts of a rotational motion apparatus.
A rotational motion apparatus consists of a shaft through which a threaded rod is mounted. Some metal
cylinders are mounted on the threaded rod and the string wrapped around the shaft in order to apply a
force to cause the system to rotate. The string is placed over the pulley so that the force applied is from
a vertically hanging mass.

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Results and Data Analysis
This experiment is designed and implemented to be able to quantitatively develop the relationship
between angular acceleration and the applied torque on the system.
From this experiment the mass, height and the time data were collected and used to determine the
angular acceleration and the torque as shown below.
The following relationship was used to obtain the acceleration
𝑎 =
𝑧∆𝑦
𝑡2
𝛼 = 𝑎/𝑟𝑠
While the torque 𝜏 can be be calculated using tension T in the string as shown below.
𝜏 = 𝑟𝑠 𝑇 = 𝑟𝑠 𝑚ℎ 𝑔
Given that 𝑟𝑠 = 17.5 𝑐𝑚 = 0.175 𝑚
Table 1: Experimental results
Mass (Kg) Height(m) Time (s) Acceleration (𝜶) 𝝉
0.50 0.98 61.81 2.9316 × 103 0.8584
0.70 0.98 45.11 5.5039× 103 1.2017
0.90 0.98 36.94 8.2080× 103 1.5451
1.10 0.98 31.08 1.1595 × 103 1.8884
1.60 0.98 28.57 1.3721 × 103 2.7468
From the collected data, a graph of acceleration against torque was obtained as shown below.
From the above relationship we can observe that torque and angular acceleration have a linear
relationship of 𝑦 = 159.34𝑥 + 0.3109
y = 159.34x + 0.3109
0
0.5
1
1.5
2
2.5
3
0.00E+00 2.00E-03 4.00E-03 6.00E-03 8.00E-03 1.00E-02 1.20E-02 1.40E-02 1.60E-02
Torque
Acceleration
Acceleration Vs Torque

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Conclusion
From the results obtained above we can confidently conclude that the aim of this experiment was
successfully achieved and the results obtained were in accordance with the theoretical expectation of
the relationship between the angular acceleration and the torque. It was found that the angular
acceleration and the torque have a linear relationship.