♪♪
(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.