 ## Physics

Learn the toughest concepts covered in Physics with step-by-step video tutorials and practice problems by world-class tutors

8. Centripetal Forces & Gravitation

# Period and Frequency in Uniform Circular Motion

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concept

## Circumference, Period, and Frequency in UCM 5m
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example

## Windmill RPMs 2m
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Hey, guys, let's check out this problem here. We're giving some information about windmill blades were told that they spin at a rate of revolutions per minute. And what we want to do is, at this rate, how long? Which is really just a time. Does it take for a windmill blade to complete one full rotation? So let's check this out. If you're ever unsure of what variable that is, just go ahead and write it down. How long a time is really has a unit of a second, so we're calculating the number of seconds to complete a full rotation. So that's the number of seconds per number of cycles or rotations, whatever they have you, and remember that seconds per cycle is actually the period. So that's what we're trying to find here. What is the period if we have these blades spinning at 20 revolutions per minute? So if you take a look at our equations, we know that there's a shortcut to calculate the period. You can just take one over the frequency. Remember that these things are basically just in verses of each other. All you have to do is flip the fraction So what happens is so we want to calculate the period and then so we're gonna have to calculate the frequency. So the frequency, remember, it's just the opposite, the inverse fraction of that which is really just the number of cycles divided by the number of seconds. So if you take a look at our problem here, do we have cycles per second? And we actually don't. We have actually 20 revolutions per minutes. So basically what happens is that whenever whenever you're given revolutions per minute, which is an rpm, it's a pretty common unit that you'll see in these problems. All you have to do is just to get to frequency. You're just going to divide that rpm by 60 the revolutions per minutes if you want. In revolutions per second, all you have to do is just divide by 60 seconds because that's how many are in a minute. So really, what happens here is to get the frequency we're gonna do 20 rpm. So this is our PM divided by 60 and you're going to get 1/3. So that's basically one third and one of the units for that or hurts. Now, remember The reason we calculate this frequency is because once we get this as a fraction or whatever number it is, all we have to do is just take one over that number. So now we can figure out the period. The period is really just Well, if we're taking one third, that's our hurts. Once you flip the fraction, it really just becomes 3/1 and that's just three seconds. And so basically, it just takes three seconds for these blades to complete a full rotation. Alright, so that's really all there is to it. So let me know if you guys have any questions.
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concept

## Equations for Velocity and Acceleration in UCM 5m
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Problem

A 3kg rock spins horizontally at the end of a 2m string at 90 RPM. Calculate its centripetal acceleration.

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example

## Spinning Space Station 3m
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