Period, Frequency, and Rotational Velocity
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- Hannah Pearson
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1 Circular Motion In this chapter we will study the motion of objects traveling in circular paths.,, and Rotational Velocity In previous chapters, we have considered objects at rest and objects moving in straight paths. What do you think are some of the differences are between 'linear' and 'circular' motion? Return to Table of Contents Jul 25 9:23 M Circular Motion One of the main differences between linear and circular motion is that circular motion repeats! This difference can change the way we think about motion a little: For instance, instead of measuring the total time it takes for an object to get from point to point, we can measure the time it takes to go around a circle once. The time it takes for an object to complete one trip around circular path is called its. The symbol for is "T" s are measured in units of time we will use seconds (s). Often we are given the time (t) it takes for an object to make a number of trips (n) around a circular path. In that case, 1 What is the period of the second hand on a clock? 60 seconds 1 hour C 12 hours The time D it depends on the time nswer The number of trips Fjfz04 1
2 2 What is the period of the minute hand on a clock? 3 What is the period of the hour hand on a clock? 60 seconds 60 seconds 1 hour 1 hour C 12 hours C 12 hours D it depends on the time D it depends on the time nswer nswer s 4 If it takes 50 seconds for an object to travel around a circle 5 times, what is the period of its motion? 5 If a runner can make a full trip around a small track in 90 seconds, how much time would it take to complete 6 loops of the track? nswer nswer If an object is traveling in circular motion and its period is 3.0s, how many revolutions will it complete in 1 minute? nswer [This object is a pull tab] nother useful measurement in circular motion is how often a cycle repeats. The number of revolutions that an object completes in a given amount of time is called the frequency of its motion. The symbol for frequency is "f" and the units we measure with are "Hz" (hertz) 2
3 Often we are given the time (t) it takes for an object to make a number of revolutions (n). In that case, 7 n object travels around a circle 50 times in ten seconds, what is the frequency (in Hz) of its motion? number of revolutions The time nswer common example of frequency can be seen on the dashboard of a car, noting revolutions per minute (rpm) of the engine crankshaft. 8 If a wheel spins with a frequency of 8 Hz, how much time will it take to spin around 16 times? 9 If an object is traveling in circular motion with a frequency of 7.0 Hz, how many revolutions will it make in 20s? nswer nswer and and We can relate them mathematically: These two equations look similar. In fact, they are exactly opposite one another. is the inverse of is the inverse of nother way to say this is that they are inverses. 3
4 10 n object has a period of 4.0s. What is the frequency of its motion? 11 n object is revolving with a frequency of 8.0 Hz. What is its period? nswer nswer Nov 29 11:00 M 4
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