Why does angle affect period pendulum

The mass of the bob does not affect the period of a pendulum because as Galileo discovered and Newton explained , the mass of the bob is being accelerated toward the ground at a constant rate — the gravitational constant, g. Just as objects with different masses but similar shapes fall at the same rate for example, a ping-pong ball and a golf ball, or a grape and a large ball bearing , the pendulum is pulled downward at the same rate no matter how much the bob weighs.

Finally, the angle that the pendulum swings through a big swing or a small swing does not affect the period of the pendulum because pendulums swinging through a larger angle accelerate more than pendulums swinging through a small angle. This is because of the way objects fall; when something is falling, it keeps accelerating. As long as an object is not going as fast as it can, it is speeding up. Therefore, something that has been falling longer will be going faster than something that has just been released.

A pendulum swinging through a large angle is being pulled down by gravity for a longer part of its swing than a pendulum swinging through a small angle, so it speeds up more, covering the larger distance of its big swing in the same amount of time as the pendulum swinging through a small angle covers its shorter distance traveled.

Watch this activity on YouTube. Ask the students to explain which factors might affect the period of a pendulum. Answer: Pendulum length, bob weight, angle pendulum swings through. Which factor s really do affect the pendulum's period?

Answer: The length of the pendulum. Why does the weight not make a difference? Answer: Because the pendulum, just like falling objects, is not dependent on weight. How does the length of a pendulum's string affect its period?

Answer: A pendulum with a longer string has a longer period, meaning it takes a longer time to complete one back and forth cycle when compared with a pendulum with a shorter string. Also, the pendulum with the longer string has a lower frequency, which means it completes less back and forth cycles in a given amount of time as compared with a pendulum with a shorter string.

Why does the angle the pendulum starts at not affect the period? Answer: Because pendulums that start at a bigger angle have longer to speed up, so they travel faster than pendulums that start at a small angle. One oscillation is complete when the bob returns to its starting position.

Count the votes and write the totals on the board. Give the right answer. Human Matching: On ten pieces of paper, write either the term or the definition of the five vocabulary words.

Ask for ten volunteers from the class to come up to the front of the room, and give each person one of the pieces of paper. One at a time, have each volunteer read what is written on their paper. Have the remainder of the class match term to definition by voting.

Have student "terms" stand by their "definitions. As a library research project, have the students research Galileo Galilei. What other scientific findings did he make during his lifetime? Have the students' research the ways that engineers use pendulums today. Some suggestions: seismographs, inertial dampeners, in sky-scrapers. Gamow, George. The Great Physicists from Galileo to Einstein. Wolfson, Richard and Jay M. Physics: For Scientists and Engineers. Note: Make sure that the groups understand that by changing the value of only one variable at a time mass, starting angle, or length , they can determine the effect that it has on the rate of the pendulum's swing.

Also, students should be sure the measurements with all the variables are reproducible, so they are confident about and convinced by their answer. After students have completed the experiments, discuss their original predictions on the activity sheet and compare them with their conclusions based on the data and the results of the tests. Older students should probably learn how the downward force of gravity on the bob is split into a component tangential to the circle on which it moves and a component perpendicular to the tangent coincident with the line made by the supporting string and directed away from the support.

The tangential force moves the bob along the arc and the perpendicular force is exactly balanced by the taut string. Now, based on these observations, determine what conclusions students can make about the nature of gravity. Students should conclude that gravitational force acting upon an object changes its speed or direction of motion, or both. If the force acts toward a single center, the object's path may curve into an orbit around the center.

Assess the students' understanding by having them explore the Pendulums on the Moon lesson, found on the DiscoverySchool. Students should click the link for "online Moon Pendulum," found under the "Procedure" section of the lesson. This activity simulates the gravitational force on the moon. Students should experiment for approximately minutes, changing the mass, length, and angle to observe the effect it has on the pendulum. Make Coupled Resonant Pendulums This experiment demonstrates that two pendulums suspended from a common support will swing back and forth in intriguing patterns if the support allows the motion of one pendulum to influence the motion of the other.

The directions for this experiment are on the Exploratorium website. Measuring Falling Time When Galileo was studying medicine at the University of Pisa, he noticed something interesting about the periods of a pendulum.

In church one day, he watched a chandelier swing back and forth in what seemed like a steady pattern of swings. He timed each swing and discovered that each period was the same length same amount of time. In the previous activity, students measured the periods of their pendulums using either digital watches or stopwatches. Galileo did not have these tools, so he used his pulse. In this activity, students will time the periods of their pendulums using their pulses and compare their results with those obtained with a watch.

Show students how to find their pulse by pressing two fingers on the artery next to their wrist. Make sure that students have been at rest for several minutes before doing this so that they can obtain a steady pulse rate. Working in teams, have one student set the pendulum in motion while another measures the pulse beats that occur during five complete swings and then ten complete swings.

Students should reproduce the distances they used in the earlier experiment, Testing Falling, for the amplitude and length of string. Record the number of pulse beats. Repeat this procedure with different students measuring their pulse rates. Then have students measure and record five complete swings and ten complete swings using a stopwatch or digital watch.

Share each group's results with the entire class. How do the pulse beat measurements compare with those timed with a watch? What are the advantages of using a stopwatch or digital watch over counting pulse beats as a method of timing? See the Tool. See the Collection.

The period is completely independent of other factors, such as mass. Even simple pendulum clocks can be finely adjusted and accurate. Note the dependence of T on g.

If the length of a pendulum is precisely known, it can actually be used to measure the acceleration due to gravity. Consider Example 1. What is the acceleration due to gravity in a region where a simple pendulum having a length We are asked to find g given the period T and the length L of a pendulum. This method for determining g can be very accurate.

This is why length and period are given to five digits in this example. Knowing g can be important in geological exploration; for example, a map of g over large geographical regions aids the study of plate tectonics and helps in the search for oil fields and large mineral deposits.

Use a simple pendulum to determine the acceleration due to gravity 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.

Calculate g. How accurate is this measurement? How might it be improved? An engineer builds two simple pendula.

Both are suspended from small wires secured to the ceiling of a room. If the initial angle is smaller than this amount, then the simple harmonic approximation is sufficient. But, if the angle is larger, then the differences between the small angle approximation and the exact solution quickly become apparent.

In the animation below left, the initial angle is small. The dark blue pendulum is the small angle approximation, and the light blue pendulum initially hidden behind is the exact solution. For a small initial angle, it takes a rather large number of oscillations before the difference between the small angle approximation dark blue and the exact solution light blue begin to noticeable diverge.