- Good morning!
Let's do a problem where
we determine centripetal acceleration.
Bobby, please read the problem,
and Bo, please translate.
♫ Flipping Physics ♫
- A cylindrical space station with a radius of 115 meters
is rotating at 0.292 radians per second.
- Stop.
Radius equals 115 meters and
angular velocity equals 0.292 radians per second.
Bobby, please.
- A ladder goes from the rim to the center.
What is the magnitude of the centripetal acceleration at,
one, the top of the ladder,
two, the middle of the ladder,
and three, the base of the ladder?
- Okay so, centripetal acceleration equals question mark
for each of those locations.
The radius I gave before of 115 meters is for part three.
The radius for part two is half way up the ladder
or 115 divided by two.
Which is 57.5 meters.
And the radius for part one is zero.
- Billy please solve all three parts.
- Okay, centripetal acceleration
equals tangential velocity squared
divided by radius,
and centripetal acceleration also equals
radius times angular velocity squared.
Because the space station's velocity
was given in radians per second,
we know 0.292 radians per second
is an angular velocity.
Therefore, we should use
radius times angular velocity squared
for the centripetal acceleration.
For part one, that means the centripetal acceleration
equals zero times,
well it doesn't matter with the angular velocity is.
The centripetal acceleration
at the top of the ladder equals zero.
The centripetal acceleration for part two
equals 57.5 times
0.292 squared.
Which is 4.90268
meters, radians squared,
over seconds squared.
And radians have no units
so it's just 4.90 meters per second squared,
with three significant digits.
The centripetal acceleration for part three equals
115 times 0.292 squared,
which is 9.80536,
or 9.81 meters per second squared,
with three significant digits.
- 9.81 meters per second squared.
Nice one Mr P.
- The acceleration due to gravity here on planet Earth.
- Nice.
- Yes, when I stand on the interior rim
of this rotating space station,
I experience a centripetal acceleration
equal to the acceleration due to gravity,
here on planet Earth.
This is called artificial gravity.
I actually feel as if I weigh
exactly what I normally do on Earth.
This concept has been shown in all sorts of movies,
for example, 2001:A Space Odyssey,
which was released in 1968
has a rotating space station for artificial gravity,
and shows Doctor Dave Bowman exercising
while jogging on the space stations interior rim.
Another movie, Elysium,
features a giant rotating space station,
with permanent residence living on it's interior rim.
Using a rotating cylindrical space station,
we can create artificial gravity.
Pretty cool, eh?
- Yeah that is pretty cool.
- Absolutely.
- But realize the jogging scene
does not take place on Space Station Five,
it takes place inside the Discovery One ship,
which is on the way to Jupiter.
And it's not Doctor Bowman,
but his crewmate, Doctor Frank Poole,
who is jogging in the scene.
Also, it said in the movie that Space Station Five
generates artificial gravity equal
to the moon's gravity to allow travelers
to acclimatize to the low gravity.
- [Mr P] Thanks Billy, sorry about the misinformation.
- It's okay.
- Okay, back to our cylindrical space station.
What will I feel when I start climbing up the ladder?
- Well, the radius decreases as you go up the ladder,
- So the centripetal acceleration,
or the artificial gravity also decreases.
- As you climb the ladder you feel like you weigh less?
- Yes. As I climb the ladder,
the centripetal acceleration,
which is causing the artificial gravity, decreases.
Which means, I feel as if my weight is decreasing.
But then what happens at the top of the ladder,
when I let go of the ladder?
- You just float there.
- Exactly, because there
the centripetal acceleration is zero,
I will feel weightless.
And will, relative to the rest of the space station,
just float there, right next to the ladder.
But I should tether myself to the ladder
because if I accidentally give myself the slightest push,
I will slowly float away from the ladder,
until I reach the outside of the space station,
and I will have almost zero tangential velocity,
but the tangential velocity of the rim of the space station
is roughly 120 kilometers per hour,
or 75 miles per hour.
Thank you very much for learning with me today,
I enjoyed learning with you.