What Is Circular Motion? | Physics in Motion

Summary

In this episode of 'Physics In Motion,' Adrian Monte explores the physics behind circular motion, focusing on acceleration and centripetal force. He explains that any object moving in a circle is accelerating due to the continuous change in direction. Monte uses examples like swinging a bucket of water and roller coasters to illustrate concepts like centripetal force, tangential velocity, and centripetal acceleration. He also clarifies the misconception of centrifugal force, attributing the sensation during a sharp turn to inertia and Newton's First Law. The segment is packed with practical demonstrations and explanations that make physics concepts engaging and relatable.

Takeaways

• 🔄 Objects moving in a circle are always accelerating due to the continuous change in direction, even if the speed is constant.
• 📉 Velocity is a vector quantity that includes both magnitude and direction; any change in either results in acceleration.
• 💧 Centripetal force, directed towards the center of the circle, is responsible for keeping an object in circular motion and can be caused by various forces such as friction, tension, normal force, or gravity.
• 🪣 Swinging a bucket of water without spilling illustrates the concept of centripetal force, where the water's inertia is balanced by the tension in the rope.
• 📚 In a free body diagram, specific forces causing centripetal motion like gravity and tension are indicated, not the centripetal force itself.
• 🌐 At the bottom of a circular path, the normal force from the bucket's surface keeps the water moving in a circle, overcoming gravity.
• 🚀 For a satellite orbiting Earth, gravity acts as the centripetal force, pulling it towards Earth and maintaining its circular orbit.
• 🛤️ On a circular track, frictional force helps the tires grip, allowing the cart to maintain a circular path with vertical forces canceling out.
• 🚗 When making a sharp turn, the sensation of being pushed against the car's side is due to inertia, not centrifugal force, as the body resists the change in motion.
• 🎢 In uniform circular motion, the tangential velocity (V_t) is constant, and the period of revolution (T) measures the time for one complete circle.
• 📐 Centripetal acceleration is calculated as the square of the tangential velocity divided by the radius of the circle and is always directed towards the center of the circle.
• 🧩 The normal force experienced during a roller coaster ride can be significantly higher than the force of gravity, as demonstrated by the example where the normal force is calculated to be 893 Newtons compared to the typical 490 Newtons when standing.

Q & A

What is centripetal force?

Centripetal force is any force that causes an object to move in a circular path. It is directed towards the center of the circle around which the object moves and is often referred to as a 'center-seeking' force.

Why is an object moving in a circular path considered to be accelerating?

An object moving in a circular path is considered to be accelerating because its direction is constantly changing, even if its speed remains constant. Acceleration is defined as a change in velocity, and velocity includes both speed and direction.

What are some examples of forces that can act as centripetal forces?

Examples of forces that can act as centripetal forces include friction, tension, the normal force, and gravity. Any of these forces can cause an object to move in a circular path.

How does the force of gravity affect an object moving in a circular path?

The force of gravity acts downward on an object moving in a circular path, such as a satellite orbiting Earth. Gravity serves as the centripetal force that pulls the object toward the center of the circular path, keeping it in orbit.

What is the difference between centripetal force and centrifugal force?

Centripetal force is a real force that acts toward the center of a circular path, keeping an object in motion along that path. Centrifugal force, on the other hand, is not a real force but rather a perceived force that appears to push an object outward when it is in a rotating reference frame. It is actually the result of inertia.

Why does water stay in a bucket when it is swung in a circular motion?

Water stays in a bucket when it is swung in a circular motion due to centripetal force. The normal force from the bottom of the bucket acts on the water, keeping it moving in a circular path. If there were no force pulling it toward the center, the water would spill out due to inertia.

What happens to an object in circular motion if the centripetal force is suddenly removed?

If the centripetal force is suddenly removed, the object would move in a straight line tangent to the circular path. This is due to tangential velocity, which is the direction the object was moving at the moment the centripetal force ceased.

How is the period of revolution related to circular motion?

The period of revolution, denoted as 'T,' is the time it takes for an object to complete one full circle along its circular path. It is a measure of the time taken for a complete cycle of motion.

What is tangential velocity and how is it related to circular motion?

Tangential velocity is the linear speed of an object moving along a circular path. It is tangent to the circular path at any given point. For uniform circular motion, the tangential speed remains constant, but its direction continuously changes as the object moves along the circle.

How do you calculate centripetal acceleration?

Centripetal acceleration is calculated using the formula 'a_c = v^2 / r', where 'v' is the tangential velocity and 'r' is the radius of the circular path. Centripetal acceleration is always directed toward the center of the circle.

Outlines

00:00

🔄 Understanding Circular Motion and Centripetal Force

This paragraph delves into the physics of circular motion, explaining that any object moving in a circle is accelerating because its direction is constantly changing, even if its speed remains constant. The concept of centripetal force, which is the net force that keeps an object moving in a circular path, is introduced. Examples of different types of centripetal forces, such as friction, tension, the normal force, and gravity, are provided. The paragraph uses the example of swinging a bucket of water to illustrate how centripetal force works, with a detailed explanation of the forces acting on the bucket and the water at different points in the swing. It also discusses how these principles apply to other scenarios, such as satellites orbiting Earth and cars making sharp turns.

05:00

🌀 Exploring Tangential Velocity and Centripetal Acceleration

The second paragraph continues the exploration of circular motion by focusing on tangential velocity and centripetal acceleration. It explains that tangential velocity is the speed of an object moving in a circle and is a vector quantity with both magnitude and direction. The period of revolution, or the time it takes for an object to complete one full circle, is introduced, along with the formula for calculating tangential velocity. The concept of centripetal acceleration, which is the acceleration experienced by an object moving in a circle due to the change in direction, is also explained. An example involving a roller coaster ride is used to demonstrate how to calculate the normal force experienced by a person at the bottom of a loop, using the principles of centripetal acceleration and Newton's Second Law. The paragraph concludes with a practical application of these concepts in the context of a roller coaster ride, highlighting the increased normal force felt at the bottom of the loop compared to standing on the ground.

Keywords

💡Acceleration

Acceleration is defined as the rate of change of velocity with time, and it occurs whenever there is a change in the magnitude or direction of velocity. In the context of the video, it is used to explain circular motion where, even at constant speed, the direction of movement is continuously changing, thus there is acceleration. An example from the script is when Adrian Monte discusses moving in a circle on a ride and how this constitutes acceleration due to the continuous change in direction.

💡Velocity

Velocity is a vector quantity that describes the rate of change of an object's position. It includes both magnitude (speed) and direction. The video script uses the concept of velocity to explain circular motion, emphasizing that a change in either magnitude or direction results in a change in velocity. An example is provided when discussing the bucket of water being swung in a circle, where the water's velocity changes due to the change in direction.

💡Centripetal Force

Centripetal force is the net force acting on an object that is required for it to follow a curved path. It is always directed towards the center of the circular path. The script introduces the term 'centripetal force' with the acronym F sub C and explains its role in various scenarios, such as swinging a bucket of water, where the tension in the rope and gravity combine to create the centripetal force that keeps the bucket moving in a circle.

💡Tangential Velocity

Tangential velocity, denoted as V sub T in the script, is the component of velocity that is tangent to the circular path. It is the speed at which an object moves along the circular path. The video explains that if the tension in the rope is released, the bucket would move in the direction of the tangential velocity, which is a straight line tangent to the circle at the point of release.

💡Inertia

Inertia is the resistance of any physical object to any change in its velocity. It is a property of matter that is quantified by mass. In the script, inertia is discussed in relation to the sensation experienced when making a sharp turn in a go-kart, where the body tends to continue in a straight line due to inertia, while the go-kart turns, causing the body to be pushed against the side of the vehicle.

💡Centrifugal Force

Centrifugal force is often misconceived as a real force; however, the script clarifies that it is not a force but rather a perceived effect due to inertia when an object is in rotational motion. The example given is the feeling of being pushed against the side of a car during a sharp turn, which is actually due to the car's acceleration towards the center of the turn, not a centrifugal force.

💡Normal Force

The normal force is the support force exerted by a surface that supports the weight of an object resting on it. In the context of the video, the normal force is what keeps the water in the bucket when swinging it in a vertical circle. At the bottom of the loop, the normal force from the bucket's bottom acts against gravity and tension to keep the water in place.

💡Uniform Circular Motion

Uniform circular motion refers to circular motion in which the object moves at a constant speed. The script explains that even though the speed (magnitude of velocity) is constant, the direction is continually changing, which means the object is still accelerating. This acceleration is known as centripetal acceleration.

💡Centrifugal Force (Misunderstanding)

The script addresses a common misunderstanding about centrifugal force, clarifying that it is not an actual force but rather a perceived effect due to the inertia of an object in circular motion. This is contrasted with the real centripetal force that acts towards the center of the circle, which is necessary for circular motion.

💡Newton's Laws

Newton's Laws of Motion are foundational principles in classical physics. The script references Newton's First Law (inertia) and Newton's Second Law (F = ma) to explain phenomena such as the sensation of being pushed against the car door during a turn and the calculation of normal force during circular motion. These laws help to understand the dynamics of objects in motion, particularly in the context of circular paths.

💡Free Body Diagram

A free body diagram is a graphical representation used to visualize all the forces acting on an object. The script uses free body diagrams to illustrate the forces at play when swinging a bucket of water and when a person is in a roller coaster loop. These diagrams help to identify the specific forces contributing to centripetal motion and to calculate the resultant forces, such as the normal force experienced by a person in a roller coaster.

Highlights

The concept of circular motion and acceleration is introduced, explaining that constant speed in a circle still involves acceleration due to the change in direction.

Velocity is defined as a vector quantity with both magnitude and direction, and any change in these results in acceleration.

Centripetal force, the force that keeps an object moving in a circle, is explained with the example of swinging a bucket of water.

Different types of centripetal forces such as friction, tension, normal force, and gravity are discussed.

The importance of the net force in creating centripetal force and its role in circular motion is highlighted.

A free body diagram of a bucket at the top of its swing is used to illustrate the forces acting on it, including gravity and tension.

The role of tension and gravity in creating the centripetal force that keeps the bucket moving in a circle is explained.

The forces at play when the bucket is at the bottom of the loop are discussed, including the normal force and its effect on the water.

The concept of inertia and how it affects the water's motion within the bucket, especially in the absence of gravity, is introduced.

The tension of the rope as the centripetal force for a bucket in space is contrasted with the role of Earth's gravity for a satellite in orbit.

Frictional force as a centripetal force that helps keep a cart in a circular path on a track is explained.

Centrifugal force is debunked as a real force, and the effect of inertia during a sharp turn is described.

The tangential velocity of an object in uniform circular motion and its relation to the period of revolution is discussed.

The calculation of centripetal acceleration using the formula involving tangential velocity and the radius of the circle is introduced.

An example problem involving a roller coaster loop and the calculation of the normal force experienced is presented.

The difference between the normal force experienced at the bottom of a roller coaster loop and standing on the ground is highlighted.

The 'Physics In Motion' toolkit is promoted for additional learning resources in physics.

Transcripts

♪♪

(Adrian Monte) We had to come up with a good excuse

to visit Wild Adventures.

This place is full of reasons to learn about physics,

starting with going in a circle.

♪♪

What if I'm moving in a circle on this ride

at a constant speed?

How am I accelerating?

Any time an object is traveling in a circular path

it is accelerating

because its direction is constantly changing.

Now remember, velocity is a vector.

It has magnitude and direction.

If either changes, velocity changes

and acceleration is defined as a change in velocity.

Let me show you an example.

You ever wonder why you can swing a bucket of water

like this...

and the water doesn't spill out?

It's because of centripetal force.

It's a word that means "center seeking"

and it's written F sub C.

Centripetal force is any force that makes an object move

in a circle.

There's more than one kind of centripetal force,

Friction, tension, the normal force, or gravity,

and any of these can act as centripetal forces

if they cause the object to move in a circle.

Here's another way to say it.

Centripetal force is the net force acting on objects

that keep them moving in a circle.

When I swing the bucket, there are two questions:

Which force makes the bucket move in a circle

and what keeps the water in the bucket?

It's a fine balance here in keeping the water

in the bucket.

So what forces are acting on the water in the bucket?

Well, let's draw a free body diagram of the bucket first

when it's at the top of the swing.

The force of gravity, F sub G, acts down.

Tension, F sub T, acts down on the bucket as well.

The force of gravity will act down regardless

but the tension force will always act

toward the center of the circle.

In this example,

the tension force and the force of gravity

create the net force,

and together, they make the bucket

seek the center of the circle

through the centripetal force.

In a free body diagram,

you don't write centripetal force per se.

You write in the specific force, or forces,

causing the centripetal motion.

In this case, gravity and tension.

So what forces make up the centripetal force

when the bucket is at the bottom of the loop?

You can see that the tension force still acts

towards the center

and gravity continues to act down

toward the Earth.

So what keeps the water in the bucket?

It's the normal force of the bucket

on the water's inertia.

Tension keeps the bucket moving in a circle.

The water within the bucket experiences

the normal force from the bottom.

This force keeps the water moving in a circle.

If we were in the middle of space

and there was no gravity,

the water would still stay in the bucket

as it was swinging in a circle

thanks to the normal force.

And what force keeps the bucket going in a circle?

Well, that's easy.

It's the tension of the rope.

Okay, what if there's no rope?

For example, what force keeps a satellite

orbiting the Earth?

It's gravity that pulls the satellite toward Earth

and keeps it in orbit,

so the centripetal force is Earth's gravity.

It's the tether that keeps the satellite

orbiting around a central point

instead of flying off into space,

but keep in mind it has to be going at

a certain velocity to stay in orbit.

If the satellite slows,

it will give way to Earth's gravity

and fall to Earth.

So let's take a few circles around this track.

The only difference between this

and the bucket of water swinging in circles,

the bucket of water swings in vertical circles.

The circle we're traveling in here is horizontal,

but the good news is the same principles apply.

So based on that, what forces keep this cart

moving around the circular track?

Frictional force is at work

helping the tires grip the track

and keeping the cart in a circular path.

Vertical forces on the cart cancel out.

The cart is center seeking

only in the horizontal direction.

And how about when you make a sharp right turn

and your body is slammed up

against the left side of the car,

what causes that?

Is it centrifugal force?

Absolutely not.

Turns out centrifugal force is not a force at all.

The real reason is explained by Newton's First Law.

Just like the water in the bucket,

your body wants to stay in the same motion

except the go-kart is turning to the right.

Your body is resisting the change

of the circular motion

and wants to continue in a straight line.

That's inertia.

So the force you feel is the car running into you

as it seeks the center of the circular path

in which it is traveling.

Okay, so let's go back to our rotating bucket of water.

We know why the water stays in the bucket.

It's experiencing uniform circular motion.

That's when an object moves in a circular path

at a constant speed.

Now, what do you think will happen to the bucket

if I were to let go of the rope?

What direction will the bucket move?

The bucket's velocity is called tangential velocity,

V sub capital T,

because if tension lets up at any given moment

the object flies in a straight line

that's tangent to the circle.

So the direction of tangential velocity

changes constantly as the object travels

in a circular path.

To measure how long it takes for the object

to go in a full circle,

that's called its period of revolution,

capital T,

or simply the period measured in seconds.

Let's go to another ride.

Recall from another segment that velocity

is a vector quantity.

It has direction and magnitude.

The magnitude of V is speed,

which is constant for uniform, circular motion,

but we will call it our tangential velocity

since this speed

and the tangential velocity magnitude

have the same value.

This ride does one full circle.

The distance traveled is called the circumference

and is calculated by multiplying the radius

by (2)pi.

And the time it takes to make a full circle

is called the period.

You write that as capital T.

The tangential velocity of an object traveling in a circle

is the distance around the circumference

divided by the time it takes to travel

around the circle once, which is the period T.

And remember, if an object is moving

in uniform, circular motion

it is accelerating,

because its direction is constantly changing.

This is called centripetal acceleration.

Centripetal acceleration is equal to

the tangential velocity squared

divided by the radius of the circle

that the object traces out.

Centripetal acceleration is always perpendicular

to the tangential velocity

and always acts in the same direction

as the centripetal force

that's causing the object to move in a circle

toward the center.

Think of Newton's Second Law.

An object will accelerate in the direction

of the net force acting on it.

In this case, the sum of the centripetal forces

is equal to the mass of the object moving in a circle

times the centripetal acceleration.

Okay, here's an example.

Imagine you're riding a roller coaster

through the bottom of a circular loop.

The loop's radius is 15 meters

and your tangential velocity at the bottom

is 11 meters per second.

If your mass is 50 kilograms,

what is the normal force exerted on you?

Drawing a free body diagram,

we see that the two forces acting on you at that moment

are gravity down and the normal force up.

By Newton's Second Law,

we can write that the normal force minus gravity

equals your mass times centripetal acceleration.

Since centripetal acceleration equals

tangential velocity squared divided by the radius,

then you can substitute that

to the right side of the equation.

And to find out the normal force,

rearrange the equation

and since the force of gravity

is mass times acceleration due to gravity

you can substitute M times G

for F sub gravity.

Now plug in the numbers

and we find that the normal force at that point

is 893 Newtons.

Compare that with the normal force you typically feel

standing on the ground,

50 kilograms times G, you get 490 Newtons.

No wonder you feel so heavy at the bottom

of the coaster loop.

That's it for this segment of "Physics In Motion."

We'll see you next time.

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and note taking guides,

check out the "Physics In Motion" toolkit.