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 1 answerLast reply by: Professor Dan FullertonTue Oct 21, 2014 7:24 PMPost by Caleb Martin on October 21, 2014Hi,How would find the "Radial Acceleration" when "A point on a rotating turntable 19.5 cm from the center accelerates from rest to a final speed of 0.800 m/s in 1.95 s. At t = 1.27 s"

### Describing Circular Motion

• Objects traveling in a circular path at constant speed are said to be in uniform circular motion.
• Average speed of an object in UCM is the distance traveled (the circumference) divided by the time it takes to travel that distance.
• The time it takes for one complete revolution is known as the period (T). Frequency (f) is the number of revolutions an object makes in one second. Frequency is the inverse of period.

### Describing Circular Motion

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Objectives 0:07
• Uniform Circular Motion 0:20
• Circumference
• Average Speed Formula Still Applies
• Frequency 1:03
• Number of Revolutions or Cycles Which Occur Each Second
• Hertz
• Formula for Frequency
• Period 1:36
• Time It Takes for One Complete Revolution or Cycle
• Frequency and Period 1:54
• Example 1: Car on a Track 2:08
• Example 2: Race Car 3:55
• Example 3: Toy Train 4:45
• Example 4: Round-A-Bout 5:39

### Transcription: Describing Circular Motion

Hi and welcome back to Educator.com0000

I'm Dan Fullerton and I would love to talk to you now about describing circular motion.0003

Our objectives are going to be to calculate the speed of an object traveling in a circular path or a portion of a circular path.0008

And also to calculate the period and frequency for objects moving in circles at constant speed.0014

So uniform circular motion has to do with an object traveling in a circular path at a constant speed.0020

First thing we have to know. The distance around the circle is its circumference.0030

That is equal to 2π times the radius of the circle.0034

Or it is also equal to π times the diameter or the diameter is the distance through the circle.0038

The average speed formula we learned from kinematics still applies.0046

If average speed is the distance travelled divided by time, for something moving in a circle you have to take into account it is 2π times the radius, the distance around the circle, divided by the time.0050

Frequency is a number which describes the number of revolutions or cycles that you can get in in 1 second.0063

So if an object travels 3 times in a circle in 1 second, it would have a frequency of 3 cycles per second, or 3 hertz.0069

H-E-R-T-Z, abbreviated Hz, where a Hertz is the same as 1 over a second.0081

The symbol for frequency is f, so frequency is the number of cycles per second, or the number of revolutions per second.0087

In similar fashion, period is the time it takes for an object to take one complete trip around the circle, or do one complete revolution or cycle.0095

Its symbol is capital T and its units are seconds. The amount of time it takes to go once around the circle.0105

Now what is really nice here is that frequency and period of course are closely related.0112

Frequency is 1 divided by the period and period is 1 divided by the frequency.0117

Once you know one, you automatically know how to figure out the other.0123

Let us take an example by looking at a car on a track.0129

Miranda drives her car clockwise around a circular track of radius 30 meters.0131

She completes 10 laps around the track in 2 minutes.0139

Let us find Miranda's total distance travelled and average speed and centripetal acceleration.0142

Well to find the distance travelled, her distance is 2π times the radius and she does 10 laps.0150

So circumference times 10 laps is going to be 2π times 30 meters, her radius times 10 laps. 300 times 2π is about 1885 meters.0160

Average speed then is the distance she travels divided by the time, or 1885 meters divided by 120 seconds, 2 minutes or 15.7 meters per second.0174

Now centripetal acceleration. That is going to describe how quickly she is accelerating.0190

Since she is moving in a circle, her velocity is changing, there must be an acceleration.0195

Centripetal acceleration, we will talk more about it later, is given by the formula v2 over r. Square the speed divided by the radius.0199

So in this case, the speed is 15.7 meters per second squared, divided by the radius of the circle, 30 meters.0209

That is going to be 8.22 meters per second squared.0219

And the direction of centripetal acceleration is always going to be toward the center of the circle.0226

All right, let us take a look at a race car problem.0234

The combined mass of a race car and its driver is 600 kilograms.0237

Travelling at constant speed, the car completes one lap around the circular track of radius 160 meters in 36 seconds.0241

Calculate the speed of the car.0253

All right, well, average speed is just distance travelled divided by the time, completes 1 lap or 1 circumference, 2πr in 36 seconds.0255

So that is going to be 2π times 160 meters over 36 seconds or about 27.9 meters per second.0266

Take a look at the toy train.0286

A half-kilogram toy train completes 10 laps of its circular track in 1 minute and 40 seconds.0288

If the diameter of the track is 1 meter, let us find the train's period and frequency.0293

Let us start with period. Period is how long it takes for 1 lap.0299

It takes it 100 seconds to go 10 laps, so the period must be 10 seconds per lap or revolution, and once we know period, frequency is easy.0304

Frequency is 1 divided by the period or 1 divided by 10 seconds which is 0.1, 1 over seconds, which is also equal to 0.1 hertz.0318

Named of course after the famous rental car company. I'm kidding.0333

Another example here, a roundabout on a playground.0339

Allan makes 38 complete revolutions on the playground roundabout in 30 seconds.0342

If the radius of the roundabout is 1 meter, let us determine the period of motion, the frequency of the motion and the speed at which Allan revolves.0347

The period of the motion, how long it takes to go once around.0364

He makes 38 revolutions in 30 seconds, so that is 30 seconds for 38 revolutions or 0.789 seconds.0367

Frequency then 1 over period, or 1 over 0.789 seconds which is 1.27 hertz.0379

And the speed at which Allan revolves.0393

Speed is distance travelled divided by the time, that is going to be 2π times the radius 1.0396

He does 38 laps, 38 times around, and the total time to do all that is 30 seconds.0403

So 2π times 1 times 38 divided by 30, I get a speed of about 7.96 meters per second.0411

Hopefully that gets you going with describing circular motion.0423

We are worried about things like speed, period, frequency and we'll tackle a little bit more about centripetal acceleration coming up quickly.0427

Thanks for watching Educator.com. Make it a great day.0435