acceleration due to gravity using a compound pendulum experiment

practical physics

Sunday 26 june 2016, experiment 10: compound pendulum.

• Plot the data in a graph similar to Fig. 2. Draw any horizontal line SS’. From the corresponding period T as determined by the ordinate of this line, and the length l of the corresponding equivalent simple pendulum as given by the average of the values of SO and S’O', calculate the acceleration g due to gravity, by means of Eq. (1) . Compare with the accepted value and record the percentage difference.
• From the mass m of the pendulum and the radius of gyration ko as determined from the graph, compute the rotational inertia Io about the axis G by Eq. (9). Compute the rotational inertia I about the axis S by Eq. (10).
• What is the minimum period with which this pendulum can vibrate? What is the length of a simple pendulum having the same period?
• Describe how Fig. 2 would be altered if the cylindrical mass M were near one end, say the end B.
• With a given, axis of suspension, say S, discuss the effect upon the period of (a) increasing the mass of the cylindrical body; (b) moving it nearer to S.
• How would the value of the minimum period To be affected by moving the mass M in either direction from the middle?
• With the mass M near the end B and the pendulum suspended about an axis S near A, how could the vibration of the system about the axis S’ be experimentally observed?
• Does the center of oscillation of a solid body, such as a rod or bar, lie within the body for any transverse axis of suspension? Explain.
• Locate the center of oscillation of a meter stick suspended about a transverse axis at the 10cm mark. At what other positions could the meter stick be suspended and have the same period?
• Prove that the period of a thin ring hanging on a peg is the same as that of a simple pendulum whose length is to the diameter of the ring.

Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to  upgrade your browser .

Enter the email address you signed up with and we'll email you a reset link.

• We're Hiring!
• Help Center

Determination of the value of g acceleration due to gravity by means of compound pendulum

There are many way of measuring this gravity acceleration, but the experiment of compound pendulum is the easiest and effective among them. In the experiment the acceleration due to gravity was measured using the rigid pendulum method. In this experiment the value of g, acceleration due gravity by means of compound pendulum is obtained and it is 988.384 cm per sec 2 with an error of 0.752%. Which is a negotiable amount of error but it needs to be justified properly.

Related Papers

Alex Francisco Estupiñán López , MIGUEL ANGEL PICO LEAL

In the course of basic physics, more precisely the course of classical mechanics should be understood as clearly as possible the subject of rotational dynamics for students of science and engineering, to have clarity with the issues concerning rotational dynamics, such as calculation of torque and forces applied to a moving system. This paper presents the implementation of a physical pendulum for the physics laboratory using mainly a bar and a disc mounted on it, which can be moved along this bar, using implements such as a flexometer to measure the different lengths and a stopwatch to take the oscillation period of the pendulum. This work shows the analytical development using the Simple Harmonic Motion (S.H.M) and experimental for the elaboration of the data collection and the realization of the laboratory with which the moment of inertia and the value of gravity could be obtained. Finally, the theoretical, experimental results and the respective errors obtained by the experiment are shown.

Journal of Physics: Conference Series

Alex Francisco Estupiñán López , Alex Francisco Estupiñán López

Searching to encourage and increase the desire of students to seek a vocation in the study of engineering and science, we wanted to implement and validate experimentally and numerically, the study of the movement of a mechanical oscillator using, in this case, a physical pendulum, formed by a bar and a disk. In this article has done the study the physical pendulum, combining a methodology that involves an experimental arrangement and the implementation of simulations developed in Python, with the aim objective of offering to students a visual and interactive experience, so that they can understand in a simpler way topics covered in the theoretical physics course, in such a way that is different from the typical physical-mathematical formalism. This study was carried out with low-cost materials and easy access, in addition to the great social impact that I had against the acceptance and assessment by the students with whom this work was applied. This work was developed in three phases: first, to measure the period of oscillation of a physical pendulum experimentally. Second, the approach of the analytical model to compare with the experimental results. Third, the development of a dynamic simulator according to the predictions of the theoretical model. The students found a didactic and different way of studying the physical pendulum. Finally, it was possible to demonstrate a self-consistency between the experimental and numerical results of the system studied in this work.

International Journal of Creative Research Thoughts - IJCRT (ISSN: 2320-2882)

Ravinder Nohtha

This research aimed to compare the standard deviation of gravitational acceleration measured by various methods. The acceleration due to gravity (g) was measured using four methods: free fall, simple pendulum, physical pendulum, and Atwood's machine. The experiments were designed for students to determine the accuracy of the results by comparing the standard deviation of experimental result to the acceleration due to gravity. The data was analyzed and the result was interpreted.

Gaziza Yeltay

salvatore ganci , Roberto De Luca

IOSR Journals

This research work is meant to investigate the acceleration due to gravity "g" using the simple pendulum method in four difference locations in Katagum Local Government Area of Bauchi State. The locations are; Rafin Tambari, Garin Arab, College of Education Azare and Township Stadium Azare. The results showed that the value of acceleration due to gravity "g" is not constant; it varies from place to place. Best on the results findings, it showed that the Rafin Tambari has the highest value of acceleration due to gravity which is (10.2 m/s 2). In difference location that I used to and Garin Arab has the lowest value of acceleration due to gravity which is (9.73m/s 2). The various results that I have found, reveals that the average value of acceleration due to gravity for Azare area of Katagum Local Government is 9.95m/s 2 which approximately equal to the accepted value of 10.0m/s 2

salvatore ganci

arXiv (Cornell University)

karla triana

Jamilu Baraya

The earth gravity pulls everything on or near the planet towards its centre. The force responsible for this pull is called the gravitational force and it varies from place to place. This paper work presents the experimental value of theoretical acceleration due to gravity g which was obtained in five (5) different locations and their average was also obtained as 9.655678 m/s, also the value of theoretical acceleration due to gravity g was obtained in that five (5) different locations where their average was obtained as 9.7897034 m/s. By comparing the two it was found that the theoretical value leads the experimental value by 0.1340254 m/s which were due to experimental errors.

Félix Hovine

Introduction The time period of a pendulum is related to its length, the longer the pendulum the longer is the time period, however you might not know that the period is also related to the gravity. If you took a pendulum to the moon, it would swing more slowly so have a longer time period. In this experiment I will measure the acceleration due to gravity on earth by measuring the time period of a pendulum

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

RELATED PAPERS

Advances in Physics Theories and Applications

ibrahim danjuma salihu

International Letters of Chemistry Physics and Astronomy

Tadeusz Hryniewicz

Rustem Kushtayev

South Florida Journal of Development

Nani Yuningsih

Progress of Theoretical Physics

Valentin Rudenko

Alessandro Germak

The Physics Teacher

Unofre Pili

Warawut Sukmak

Lat. Am. J. Phys. Educ. Vol. 3, No. 2, May 2009

Paolo Peranzoni , Giacomo Torzo

Physics Education

Khairurrijal Khairurrijal

Latresa White

Mihai Grumazescu

EDUARDO LARRINA

Muhammad Hamza

Alessandro Germak , Claudio Origlia

RELATED TOPICS

•   We're Hiring!
•   Help Center
• Find new research papers in:
• Health Sciences
• Earth Sciences
• Cognitive Science
• Mathematics
• Computer Science
• Academia ©2024

• Science Notes Posts
• Contact Science Notes
• Todd Helmenstine Biography
• Anne Helmenstine Biography
• Free Printable Periodic Tables (PDF and PNG)
• Periodic Table Wallpapers
• Interactive Periodic Table
• Periodic Table Posters
• Science Experiments for Kids
• How to Grow Crystals
• Chemistry Projects
• Fire and Flames Projects
• Holiday Science
• Chemistry Problems With Answers
• Physics Problems
• Unit Conversion Example Problems
• Chemistry Worksheets
• Biology Worksheets
• Periodic Table Worksheets
• Physical Science Worksheets
• Science Lab Worksheets
• My Amazon Books

How to Calculate Acceleration Due to Gravity Using a Pendulum

A simple pendulum is an easy way to calculate the acceleration due to gravity wherever you find yourself.

This can be accomplished because the period of a simple pendulum is related to the acceleration due to gravity by the equation

where T = period L = length of the pendulum g = acceleration due to gravity

This worked example problem will show how to manipulate this equation and use the period and length of a simple pendulum to calculate the acceleration due to gravity.

Calculate Acceleration Due To Gravity Example Problem

Question: Astronaut Spaceman uses a small mass attached to a 0.25 m length of string to figure out the acceleration due to gravity on the Moon. He timed the pendulum’s period to be 2.5 seconds. What were his results?

Start with the equation from above

Square both sides to get

Multiply both sides by g

Divide both sides by T 2

This is the equation we need to make our calculation. Plug in the values for T and L where T = 2.5 s and L = 0.25 m

g = 1.6 m/s 2

Answer: The Moon’s acceleration due to gravity is 1.6 m/s 2 .

This type of problem is easy to work out and easy to make simple errors. A common error with this problem is not squaring pi when entering the numbers into a calculator. This will result in an answer 3.14 times less than the true answer.

It is also good to keep track of your units. This problem could have had a measurement for the length at 25 cm. instead of 0.25 m. Unless you recorded your acceleration units as cm/s 2 , the m/s 2 value would be 100 times greater than the correct answer.

Other Simple Pendulum Example Problems

Check out another  simple pendulum example problem  which uses the pendulum period formula to calculate the length when the period is known. Or this example problem to calculate the period when the length is known.

Related Posts

16.4 The Simple Pendulum

Learning objectives.

By the end of this section, you will be able to:

• Measure acceleration due to gravity.

Pendulums are in common usage. Some have crucial uses, such as in clocks; some are for fun, such as a child’s swing; and some are just there, such as the sinker on a fishing line. For small displacements, a pendulum is a simple harmonic oscillator. A simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string, such as shown in Figure 16.13 . Exploring the simple pendulum a bit further, we can discover the conditions under which it performs simple harmonic motion, and we can derive an interesting expression for its period.

We begin by defining the displacement to be the arc length s s . We see from Figure 16.13 that the net force on the bob is tangent to the arc and equals − mg sin θ − mg sin θ . (The weight mg mg has components mg cos θ mg cos θ along the string and mg sin θ mg sin θ tangent to the arc.) Tension in the string exactly cancels the component mg cos θ mg cos θ parallel to the string. This leaves a net restoring force back toward the equilibrium position at θ = 0 θ = 0 .

Now, if we can show that the restoring force is directly proportional to the displacement, then we have a simple harmonic oscillator. In trying to determine if we have a simple harmonic oscillator, we should note that for small angles (less than about 15º 15º ), sin θ ≈ θ sin θ ≈ θ ( sin θ sin θ and θ θ differ by about 1% or less at smaller angles). Thus, for angles less than about 15º 15º , the restoring force F F is

The displacement s s is directly proportional to θ θ . When θ θ is expressed in radians, the arc length in a circle is related to its radius ( L L in this instance) by:

For small angles, then, the expression for the restoring force is:

This expression is of the form:

where the force constant is given by k = mg / L k = mg / L and the displacement is given by x = s x = s . For angles less than about 15º 15º , the restoring force is directly proportional to the displacement, and the simple pendulum is a simple harmonic oscillator.

Using this equation, we can find the period of a pendulum for amplitudes less than about 15º 15º . For the simple pendulum:

for the period of a simple pendulum. This result is interesting because of its simplicity. The only things that affect the period of a simple pendulum are its length and the acceleration due to gravity. The period is completely independent of other factors, such as mass. As with simple harmonic oscillators, the period T T for a pendulum is nearly independent of amplitude, especially if θ θ is less than about 15º 15º . Even simple pendulum clocks can be finely adjusted and accurate.

Note the dependence of T T on g g . If the length of a pendulum is precisely known, it can actually be used to measure the acceleration due to gravity. Consider the following example.

Example 16.5

Measuring acceleration due to gravity: the period of a pendulum.

What is the acceleration due to gravity in a region where a simple pendulum having a length 75.000 cm has a period of 1.7357 s?

We are asked to find g g given the period T T and the length L L of a pendulum. We can solve T = 2π L g T = 2π L g for g g , assuming only that the angle of deflection is less than 15º 15º .

• Square T = 2π L g T = 2π L g and solve for g g : g = 4π 2 L T 2 . g = 4π 2 L T 2 . 16.30
• Substitute known values into the new equation: g = 4π 2 0 . 75000 m 1 . 7357 s 2 . g = 4π 2 0 . 75000 m 1 . 7357 s 2 . 16.31
• Calculate to find g g : g = 9 . 8281 m / s 2 . g = 9 . 8281 m / s 2 . 16.32

This method for determining g g can be very accurate. This is why length and period are given to five digits in this example. For the precision of the approximation sin θ ≈ θ sin θ ≈ θ to be better than the precision of the pendulum length and period, the maximum displacement angle should be kept below about 0.5º 0.5º .

Making Career Connections

Knowing g g can be important in geological exploration; for example, a map of g g over large geographical regions aids the study of plate tectonics and helps in the search for oil fields and large mineral deposits.

Take Home Experiment: Determining g g

Use a simple pendulum to determine the acceleration due to gravity g g in your own locale. Cut a piece of a string or dental floss so that it is about 1 m long. Attach a small object of high density to the end of the string (for example, a metal nut or a car key). Starting at an angle of less than 10º 10º , allow the pendulum to swing and measure the pendulum’s period for 10 oscillations using a stopwatch. Calculate g g . How accurate is this measurement? How might it be improved?

Check Your Understanding

An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10 kg 10 kg . Pendulum 2 has a bob with a mass of 100 kg 100 kg . Describe how the motion of the pendula will differ if the bobs are both displaced by 12º 12º .

The movement of the pendula will not differ at all because the mass of the bob has no effect on the motion of a simple pendulum. The pendula are only affected by the period (which is related to the pendulum’s length) and by the acceleration due to gravity.

PhET Explorations

Pendulum lab.

Play with one or two pendulums and discover how the period of a simple pendulum depends on the length of the string, the mass of the pendulum bob, and the amplitude of the swing. It’s easy to measure the period using the photogate timer. You can vary friction and the strength of gravity. Use the pendulum to find the value of g g on planet X. Notice the anharmonic behavior at large amplitude.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/college-physics-2e/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units

• Authors: Paul Peter Urone, Roger Hinrichs
• Publisher/website: OpenStax
• Book title: College Physics 2e
• Publication date: Jul 13, 2022
• Location: Houston, Texas
• Book URL: https://openstax.org/books/college-physics-2e/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units
• Section URL: https://openstax.org/books/college-physics-2e/pages/16-4-the-simple-pendulum

© Jul 9, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

All Lab Experiments

To Determine the Value of Acceleration Due to Gravity (g) Using Bar Pendulum

• Physics Practical Files

Bar Pendulum Practical File in .pdf

Find more Mechanics Practical Files on this Link – https://alllabexperiments.com/phy_pract_files/mech/

Watch this Experiment on YouTube – https://www.youtube.com/watch?v=RVDTgyj3wfw

Watch the most important viva questions on Bar Pendulum – https://www.youtube.com/watch?v=7vUer4JwC5w&t=3s

Please support us by donating, Have a good day

4 thoughts on “To Determine the Value of Acceleration Due to Gravity (g) Using Bar Pendulum”

Finally found the solution of all my problems,the best website for copying lab experiments.thanks for help

Hyyyy how i download this pdf

non downloadable but free to access

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Related Posts

To find the width of the wire using diffraction pattern obtained by a he-ne laser – practical file.

This Link Contains the Practical File of this experiment in readable pdf format ...

To Study the Low Pass and High Pass RC Filters

This Link provides the handwritten practical file of the above mentioned experiment (with readings) in the readable pdf format. ...

To Study the Characteristics of a UJT (Unijunction Transistor) and Study the Working of UJT as Saw Tooth Generator

Follow along with the video below to see how to install our site as a web app on your home screen.

Note: This feature may not be available in some browsers.

• Classical Physics

Compound pendulum experiment to find the acceleration due to gravity

• Thread starter VVS2000
• Start date Mar 20, 2020
• Tags Acceleration Compound pendulum Experiment Gravity Pendulum
• Mar 20, 2020

A PF Molecule

• Floquet engineering tunes ultracold molecule interactions and produces two-axis twisting dynamics
• Experimental data help unravel the mystery surrounding the creation of heavy elements in stars
• Latent information carried by photons enables super-precise spectrometer
• Mar 21, 2020

As a pendulum gets longer the time period gets longer, so it is clear why T should be going up at the ends. When the bar is attached at its middle at the center of gravity, there is no change in gravitational potential energy as the bar swings, so there is no reason to oscillate, so T goes to infinity. Near there, with very little net torque to make it oscillate T is very large, so it is clear why it should go up in the middle. There must be a minimum in between. Another way to look at it is comparing the torque to the rotational inertia. The angular acceleration is inversely related to the period, and angular acceleration is torque / inertia. So you can see how the period changes by examining torque / inertia. Picture the bar tilted from vertical by some particular angle. The torque increases linearly as you move the suspension point away from the center of gravity. However, the inertia does not change linearly. If L is the total length of the rod and x is how far the suspension point is from the center, then the moment of inertia is ## \frac 1 3 \frac M L (\frac {L^3} 4 + 3 L x^2)## Which is parabolic in x.  

FAQ: Compound pendulum experiment to find the acceleration due to gravity

1. what is a compound pendulum experiment.

A compound pendulum experiment is a scientific experiment used to determine the acceleration due to gravity. It involves a pendulum with a rigid rod and a weight attached to it, as opposed to a simple pendulum which only has a weight attached to a string.

2. How does a compound pendulum experiment work?

In a compound pendulum experiment, the pendulum is set into motion and its oscillations are timed. The length of the pendulum, the mass of the weight, and the time it takes to complete one oscillation are used to calculate the acceleration due to gravity using the formula g = 4π²l/T², where g is the acceleration due to gravity, l is the length of the pendulum, and T is the period of oscillation.

3. What is the purpose of a compound pendulum experiment?

The purpose of a compound pendulum experiment is to accurately measure the acceleration due to gravity. This value is important in many areas of science, such as physics, engineering, and astronomy.

4. What factors can affect the results of a compound pendulum experiment?

The results of a compound pendulum experiment can be affected by various factors, such as air resistance, friction at the pivot point, and the accuracy of the timing device. It is important to minimize these factors as much as possible in order to obtain accurate results.

5. How is the acceleration due to gravity calculated from the results of a compound pendulum experiment?

The acceleration due to gravity is calculated by using the formula g = 4π²l/T², where g is the acceleration due to gravity, l is the length of the pendulum, and T is the period of oscillation. By measuring these values and plugging them into the formula, the acceleration due to gravity can be determined.

Similar threads

• May 20, 2024
• Apr 22, 2018
• Jun 29, 2024
• Aug 7, 2019
• Nov 6, 2016
• Apr 12, 2016
• Aug 8, 2017
• Jul 14, 2011
• Jan 19, 2024
• Sep 11, 2015

Hot Threads

• B   Why 186,282?
• Insights   The Slinky Drop Experiment Analysed
• B   Sine wave noise at different frequencies
• B   How does an object gain potential energy?
• B   Why Is an Object's Weight Equal to the Force of Gravity It Experiences?

Recent Insights

• Insights   Brownian Motions and Quantifying Randomness in Physical Systems
• Insights   PBS Video Comment: “What If Physics IS NOT Describing Reality”
• Insights   Aspects Behind the Concept of Dimension in Various Fields
• Insights   Views On Complex Numbers
• Insights   Addition of Velocities (Velocity Composition) in Special Relativity
• Insights   Schrödinger’s Cat and the Qbit