What Is Circular Motion? | Physics in Motion
Summary
TLDRIn 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
🔄 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.
🌀 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.
Mindmap
Keywords
💡Acceleration
💡Velocity
💡Centripetal Force
💡Tangential Velocity
💡Inertia
💡Centrifugal Force
💡Normal Force
💡Uniform Circular Motion
💡Centrifugal Force (Misunderstanding)
💡Newton's Laws
💡Free Body Diagram
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.
(announcer) For more practice problems, lab activities,
and note taking guides,
check out the "Physics In Motion" toolkit.
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