Uniform Circular Motion: Crash Course Physics #7

Summary

This video explains the physics of uniform circular motion through the example of carnival rides and NASA's human centrifuge tests. It highlights the difference between centripetal and centrifugal forces, and why centrifugal force is considered fictitious. The script covers key concepts like tangential velocity, centripetal acceleration, period, and frequency, using real-life examples and simple experiments to illustrate these principles. The goal is to show how objects move in circles and to calculate if such rides are safe for humans, emphasizing the fascinating and sometimes misunderstood nature of circular motion.

Takeaways

• 🎢 Uniform circular motion involves moving along a circular path consistently.
• ⚖️ Centripetal acceleration is directed inward, while the concept of centrifugal force is a fictitious force.
• 🚀 NASA tested astronauts' tolerance for acceleration using a human centrifuge, finding most could handle 98 meters per second squared for 10 minutes.
• 🎡 The velocity in circular motion is tangent to the circle, not along the path.
• 🔄 To demonstrate tangential velocity, you can twirl a key on a string and release it to see it fly off tangentially.
• 🌀 Centripetal force keeps an object moving in a circle, pulling it towards the center.
• 👀 From an external perspective, centripetal force is clear, while from an internal perspective, it feels like a centrifugal force.
• ⏳ The period (T) is the time it takes for one complete revolution, and frequency (f) is the number of revolutions per second.
• 📏 The circumference of the circle relates to the distance traveled in one revolution.
• 🔢 The speed in uniform circular motion can be calculated by dividing the circumference by the period.
• 📈 Centripetal acceleration magnitude is given by the speed squared divided by the radius, increasing with speed or decreasing radius.
• ✔️ Calculating safety: for a ride with a speed of 15.7 meters per second and a radius of 5 meters, the centripetal acceleration is 49.3 meters per second squared, considered safe for short periods.

Q & A

What is the experience of being on a twirly carnival ride like?

The experience is described as intense and nauseating due to the sensation of spinning in a circle, which is a form of uniform circular motion.

What is uniform circular motion?

Uniform circular motion is the movement of an object along a circular path at a constant speed, resulting in a consistent acceleration inward, known as centripetal acceleration.

Why is centripetal acceleration often misunderstood?

Centripetal acceleration is often misunderstood because people sometimes confuse it with centrifugal acceleration, which is a perceived outward force but is not a real physical force.

What was the purpose of the human centrifuge used by NASA in 1960?

The human centrifuge was used to test how much acceleration potential astronauts could withstand before they would black out, which is crucial for space flight.

What is the acceleration limit that most people can withstand for 10 minutes according to NASA's tests?

Most people can withstand an acceleration of around 98 meters per second squared for 10 minutes, which is about ten times the acceleration caused by gravity.

How is velocity in uniform circular motion different from velocity in straight-line motion?

In uniform circular motion, the velocity is always tangent to the circle, meaning its direction is perpendicular to the radius at any given point, unlike straight-line motion where the direction is constant.

What is the relationship between the centripetal force and the velocity of an object in circular motion?

The centripetal force is responsible for changing the direction of the object's velocity, keeping it moving in a circular path. It is always directed toward the center of the circle.

Why do people sometimes feel a centrifugal force when they are in a spinning ride?

The sensation of a centrifugal force is due to a change in perspective or frame of reference. From the perspective of someone inside a spinning ride, it feels like they are being pushed outward, even though it's the centripetal force pulling them inward.

What is the period of motion in uniform circular motion?

The period of motion, represented by the variable T, is the time it takes for an object to complete one full revolution around the circle and return to its starting point.

How is the frequency of motion related to the period of motion?

The frequency of motion, represented by f, is the number of revolutions per second. It is the reciprocal of the period, calculated as 1 divided by the period (f = 1/T).

What is the formula for calculating the speed of an object in uniform circular motion?

The speed of an object in uniform circular motion is calculated by dividing the distance traveled in one revolution (circumference of the circle, which is 2πr) by the time taken for one revolution (the period, T).

How is centripetal acceleration related to the speed and radius of the circular path?

The magnitude of centripetal acceleration is equal to the square of the speed divided by the radius of the circle (a_c = v^2 / r). This means that increasing the speed or decreasing the radius results in greater acceleration.

How can you determine if a carnival ride is safe based on the acceleration experienced by riders?

By calculating the centripetal acceleration experienced by riders using the formula a_c = v^2 / r and comparing it to the known safe acceleration limits, such as those tested by NASA, you can determine if the ride is safe.

Outlines

00:00

🎢 Understanding Uniform Circular Motion and Centripetal Force

This paragraph introduces the concept of uniform circular motion, often experienced on carnival rides, and its relation to Newtonian physics. It clarifies the misunderstanding between centripetal and centrifugal forces, explaining that while centripetal acceleration is real and directed inward, centrifugal force is a perceived effect due to a change in frame of reference. The paragraph also references NASA's use of a human centrifuge to test astronaut tolerance to acceleration, revealing that most people can withstand about 10 times the force of gravity for a short period. The goal is to calculate the safety of carnival rides by understanding the physics of uniform circular motion, which involves position, velocity, acceleration, and time.

05:00

🌀 Exploring the Physics of Circular Motion: Velocity, Acceleration, and Safety

The second paragraph delves deeper into the physics of uniform circular motion, explaining velocity as a vector quantity that is always tangent to the circle, indicating both speed and direction. It describes an experiment with a string and a key to demonstrate how objects in motion tend to move in a straight line unless acted upon by a force. The paragraph then discusses centripetal force and centripetal acceleration, which are responsible for the circular motion and the sensation of being pushed outward (misattributed to centrifugal force). It also covers the concepts of period and frequency in relation to circular motion, using the example of a centrifuge ride with a 2-second period. The summary concludes with the calculation of the ride's speed and the development of an equation for centripetal acceleration, which is then used to assess the safety of the ride, comparing it to the acceleration thresholds tested by NASA.

Keywords

💡Uniform Circular Motion

Uniform circular motion is a type of motion where an object moves along a circular path at a constant speed. It is central to the video's theme as it explains the physics behind the carnival rides and human centrifuges. The script uses the concept to describe the consistent movement in a circle, which is the basis for understanding the forces and accelerations involved.

💡Centrifugal Acceleration

Centrifugal acceleration is often mistakenly thought of as a real force pushing objects outward in a circular path. The video clarifies that it is a fictitious force experienced in a rotating frame of reference. It is a key concept because it helps explain the sensation riders feel on the carnival rides, even though the actual force is directed inward.

💡Centripetal Acceleration

Centripetal acceleration is the real acceleration experienced by an object in circular motion, directed towards the center of the circle. The video emphasizes its importance in understanding the physics of the rides, as it is responsible for the force that keeps objects moving in a circle, counteracting their inertia.

💡Centrifuge

A centrifuge is a device that uses centripetal force to spin objects at high speeds, pushing them outward against the wall of the spinning chamber. The video references NASA's use of a human centrifuge to test the limits of human tolerance to acceleration, tying it to the theme of understanding the physics of circular motion.

💡Inertia

Inertia is the resistance of an object to change its state of motion. The video discusses inertia in the context of an object in motion wanting to continue in a straight line unless acted upon by an external force, which is key to understanding why objects move in a circle.

💡Tangential Velocity

Tangential velocity is the component of velocity that is perpendicular to the radius of the circle and parallel to the circle's circumference. The video uses the concept to explain the direction of velocity in circular motion and how it differs from the direction of centripetal acceleration.

💡Period

The period of motion is the time it takes for an object to complete one full cycle of its path. In the context of the video, the period is used to describe the time taken for a complete revolution on the carnival ride, which is essential for calculating frequency and other motion parameters.

💡Frequency

Frequency is the number of cycles or revolutions an object makes in a unit of time. The video explains frequency as being inversely related to the period, and it is used to describe how many times the ride completes a revolution in a given time frame.

💡Circumference

Circumference is the total distance around a circle, calculated as 2π times the radius. The video uses the concept of circumference to discuss the distance covered by a rider in one complete revolution of the centrifuge ride.

💡Fictitious Force

A fictitious force is a force that appears to act on objects in a non-inertial reference frame. The video explains centrifugal force as a fictitious force, which feels real to riders on the centrifuge but does not actually exist from an external observer's perspective.

💡Safety

Safety is a critical aspect discussed in the video in relation to the acceleration experienced by riders on the centrifuge ride. The script calculates the acceleration to ensure it is within safe limits for human tolerance, tying the concept of safety to the physical forces and accelerations involved in circular motion.

Highlights

Uniform circular motion is a misunderstood concept in Newtonian physics involving centripetal acceleration.

Centrifugal acceleration is a fictitious force experienced in a rotating frame of reference but does not actually exist.

NASA tested human tolerance to acceleration using a centrifuge to prepare for space flight.

Most people can withstand an acceleration of 98 meters per second squared for 10 minutes without blacking out.

The physics of carnival rides can be analyzed using equations for uniform circular motion.

Velocity in uniform circular motion is always tangent to the circle, not along the path.

Inertia causes an object to continue moving in a straight line unless acted upon by a net external force.

Centripetal force is responsible for the circular motion and is directed toward the center of the path.

Centrifugal force is perceived from an internal frame of reference but is not a real force.

The period of motion is the time taken to complete one revolution in uniform circular motion.

Frequency is the number of revolutions per second and is the inverse of the period.

Circumference of a circle is used to describe the distance covered in one revolution.

Average velocity in uniform circular motion is calculated by dividing the distance traveled by the time taken.

Centripetal acceleration is derived from the speed squared divided by the radius of the circle.

The safety of a centrifuge ride can be assessed by comparing the experienced acceleration with human tolerance limits.

The sensation of being pushed outward in a centrifuge is due to a change in perspective, not a real force.

Crash Course Physics provides a comprehensive understanding of the physics behind carnival rides and human centrifuges.

Transcripts

Ever been on one of those twirly carnival rides?

You know, the ones where you get into a giant cylinder and stand against the wall, and then they spin you around like a wet salad?

If you've had that uniquely nauseating experience, then you know that the simple act of spinning in a circle can be ... intense.

It also happens to be one of the most misunderstood concepts in Newtonian physics.

It’s known as uniform circular motion, and it’s what occurs when anything moves along a circular path in a consistent way.

Most of the confusion about this idea has to do with the fact that things accelerate inward as they move in a circle --

a kind of acceleration known as centripetal acceleration. But you'll often hear people talking about

centrifugal acceleration pushing things outward as they move in a circle.

That's actually where centrifuges get their name! And centrifugal acceleration isn't wrong, exactly.

It's just ... not real. So, to explain how things really accelerate

when they move in circles, let's talk about the physics of that ride as it spins you around

-- assuming you're willing to risk stepping inside. I'm getting dizzy just thinking about it.

[Theme Music]

In 1960, NASA was getting ready to send people to space.

They knew that a big part of space flight would involve acceleration,

so they wanted to test how much acceleration people could handle before they'd black out.

Because that’s what happens when too much blood is forced away from your brain for too long.

So engineers tested potential astronauts by putting them in a human centrifuge --

Basically, a superpowered version of those rides at the fair.

They found that most people could withstand an acceleration of around 98 meters per second squared for 10 minutes --

That's about ten times the acceleration caused by gravity that you'd feel just by jumping in the air.

With that in mind, let's say we've been asked to calculate the safety of one of those carnival rides --

which means we'll need to figure out how much acceleration riders would experience.

There are equations we can use to do that, because just like with all the other kinds

of motion we've talked about so far, uniform circular motion has four main qualities --

position, velocity, acceleration, and time. And they're all related to each other.

When it comes to uniform circular motion, position is the most obvious quality:

There’s an object, and it’s on a circular path. But velocity is a little less intuitive.

At any given moment, velocity tells you how fast the object’s going, and in what direction.

And that direction … is NOT along the path of the circle.

It’s actually perpendicular to the radius of the circle -- along what we call a tangent.

So if you draw an arrow representing the velocity on the circle, it’ll only touch the circle in one spot.

OK bear with me here, as this might seem kinda strange, but it’s true!

One of the nice things about the physics of motion is that often,

you can just try it out for yourself and see what happens.

So here’s a quick way to see tangential velocity in action:

All you need is some string, a key -- or some other small object to tie

the string to -- and a wide open space so nobody gets hurt , by a key flying around.

Move the string so the key starts twirling around in counterclockwise circles, parallel

to the ground. Then, when the key is at the point in the circle that’s farthest away

from you… let go of the string. The key flies to the left!

Here’s why: In earlier episodes, we’ve talked about inertia and the idea that if

an object is in motion, it’ll remain in that motion unless it’s acted upon by a

net external force. Which means that something moving in a straight

line is going to continue moving in a straight line unless a force -- one that isn’t balanced

out by other forces -- turns it. Whenever you see something turning?

There’s a net external force acting on it. That’s why, at any given moment, the velocity

of an object moving in a circle will be tangent to it. Without a force to turn it, it just

flies in whatever direction it was moving last. Once you let go of the string, you got

rid of the force that was making the key turn in circles.

So it kept moving with the same velocity that it had at the exact moment you let go -- perpendicular

to the string connecting it to your hand, which was the center of the key’s circular

path. And now, we can finally talk about the mysterious force that was accelerating the

key -- changing the direction of its velocity so that it moved in a circle.

That force is the same reason riders on the human centrifuge spin in a circle -- in fact,

it’s the reason anything moves in a circle. That force is known as the centripetal force,

and the acceleration it causes is called centripetal acceleration.

And the important thing to remember about centripetal acceleration is that it’s always

directed toward the center of the circular path.

That makes a lot of sense, if you think about it in terms of how the velocity’s changing.

The key was only turning in circles because your hand was pulling it toward the center

of a circular path. But now think about what it’s like to be

on one of those centrifuge rides -- or, if you’ve never subjected yourself to one,

what it’s like to be in a car that turns sharply. The ride -- or the car -- is turning

in a circle, so there must be centripetal acceleration pushing you toward the middle

of that circle. Except, it feels like you’re being pushed

outward. People often attribute this sensation to centrifugal force. But that’s not real.

The reason that people confuse the centripetal force with what feels like a centrifugal

force comes down to a change in perspective -- what physicists call a frame of reference.

From the frame of reference of someone standing outside the human centrifuge, it’s easy

to see what’s actually happening: As the cylinder turns, it forces the people inside

it to move in a circle. And the wall is pressing on them to keep them turning -- it’s actually

pushing them toward the center of the circle! But the person inside the cylinder just sees

everything moving around with them. From their frame of reference, it feels like

they’re just being squashed against the wall -- as though there’s a centrifugal

force acting on them. But there’s nothing there to actually create

that force. Which is why physicists call it a fictitious force -- it doesn’t really exist.

So! Now that we know how acceleration works

when you’re moving in a circle, we can finally come up with some ways to connect position,

velocity, and acceleration -- and figure out if that centrifuge ride is safe for people.

But first, we have to talk about time. When something’s moving around a circle in a

consistent way -- in other words, its acceleration is constant -- it’ll take a certain amount

of time to return to its starting conditions. In this case, those starting conditions are

a particular point along the circular path. We call that time the period of the motion,

and the variable we use to represent it is a capital T.

Which isn’t too hard to remember, as long as you keep in mind that the period is an

amount of time. From timing the centrifuge ride in action, we know that it takes 2 seconds

to spin around once. So we’d say that the period of its motion is 2 seconds.

But sometimes it’s easier to talk about the same idea in another way -- how many revolutions

does the ride make in one second? That’s what we’d call the frequency of the motion

-- which we write as an f in equations. That’s simple enough to figure out: if it

takes the ride 2 seconds to make one revolution, then it’s making one half of a revolution

per second.It’s also not too difficult to relate period and frequency with an equation:

frequency is just 1, divided by the period. Now that we’ve gotten time out of the way,

let’s talk about position. We generally talk about distance in terms of the circumference

of the circle, because that tells us how many times you’ve gone around the circle.

In other words, if a centrifuge rider covers the same distance as one circumference, we

know they’ve made one revolution. And circumference is just 2 times pi times the radius of the

circle. So if that human centrifuge has a radius of 5 meters, riders would travel 31.4 meters every revolution.

Now: What about their speed? Well, in our

episodes on motion in a straight line, we talked about how average velocity is generally

equal to the change in position over the change in time -- -- which turns out to be a great

way to describe the speed of uniform circular motion.

When the rider’s made one revolution around the circle, they’ve covered a distance equal

to 2 times pi times r -- or, in this case, 31.4 meters. That’s how far they’ve traveled.

And the amount of time it took was equal to the period of the ride’s motion. That’s

their change in time. Divide the distance they’ve traveled by

their change in time, and you get the speed equation for uniform circular motion. Using

that equation, we can calculate the speed of a rider on the centrifuge -- it’s 15.7

meters per second. Next, getting the equation for the magnitude

of centripetal acceleration -- how strong it is, basically -- is a little less straightforward.

That magnitude will be equal to the change in velocity over the change in time at any given

moment -- in other words, its derivative. Actually calculating the derivative can

get complicated, but it turns out to be equal to the speed, squared, divided by the radius

of the circle. This equation makes a lot of sense for a few

reasons: First, take a look at the units. Acceleration is measured in meters per second

squared, so we already know that whatever the equation for centripetal acceleration

is, the units have to work out to meters per second squared.

And they do: square the speed, and you end up with units of meters squared per second

squared. Just divide those units by meters, and you get meters per second squared. You

can also tell from this equation that if you increase your speed along the circular path

or decrease the radius of that path, you should end up with a higher acceleration.

And that relationship between acceleration, speed, and radius checks out in real life, too:

Try spinning the key on a string faster, or shortening the string but spinning it at

the same speed. You’ll feel the key pulling harder on your fingers, because it’s experiencing

more acceleration. And now that we have an equation for the acceleration

that riders would experience on the centrifuge, we can finally figure out if that ride is

safe. We already know that their speed would be 15.7 meters per second, and that the radius

of the ride is 5 meters. So, according to the equation for acceleration,

their acceleration would be 49.3 meters per second squared. That’s about half the acceleration

that NASA found would make people black out. So the ride is probably safe, at least for

a couple of minutes. Whether that much acceleration would be pleasant is a different story -- but

hey, we’re just here to make sure the ride is safe. We’re not responsible for cleaning

up the vomit once it’s over. Today, you learned that when an object is

in uniform circular motion, its velocity is tangent to the circle and its acceleration

is pointing inward. We also talked about the difference between centripetal and centrifugal

forces, and derived equations for period, frequency, velocity, and acceleration.

Crash Course Physics is produced in association with PBS Digital Studios. You can head over

to their channel to check out amazing shows like Deep Look, The Good Stuff, and PBS Space Time.

This episode of Crash Course was filmed in the Doctor Cheryl C. Kinney Crash Course

Studio with the help of these amazing people and our equally amazing graphics team is Thought Cafe.