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32_measure_circular - Lesson 32 Measuring Circular Motion...

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Lesson 32: Measuring Circular Motion Velocity There should be a way to come up with a basic formula that relates velocity in a circle to some of the basic properties of a circle. Let’s try starting off with a formula that we know from the beginning of the course. v = d t Since we are looking at something going around in a circle, the distance it covers each revolution is equal to the circumference of the circle. C = 2 r We will substitute this into the first formula where the distance the object travels (“d”) equals the circumference (“C”)... v = 2 r t The last thing we need to change is the time “t” on the bottom. We're only interested in how much time it takes for the object to go around that circumference once, so what we really need to measure is the period of the motion, not its time. This gives us a slightly different looking formula... v = 2 r T v = velocity (m/s) π = pi, use 3.14 in your calculations r = radius of the circle (m) T = period (s) Example 1 : Determine the length of a student’s arm if she can swing a pail around five times in a circle at 2.72m/s in 7.5s. Period is the time it takes to do something once, so... T = 7.5s 5 revs = 1.5 s Then we can calculate the radius... v = 2 r T r = vT 2 r = 2.72  1.5 2 3.14 r = 0.65m 7/22/2008 © studyphysics.ca Page 1 of 5 / Section 5.2 Did You Know? The word period is also used in other sciences, such as the "Periodic Table of the Elements" in chemistry. It is named this way because periodically the elements repeat the same characteristics.
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Centripetal Acceleration We already know that the centripetal acceleration points in towards the centre of the circle.
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