- Good morning.
It is time to demonstrate the directions
of tangential velocity and tangential acceleration.
♫ Flipping Physics ♫
Let's start by looking at three mints on a turntable
of a record player.
When we plug in the record player,
it takes slightly less than one second to uniformly speed up
to its constant angular velocity
of 33 revolutions per minute.
And then, when we unplug the turntable,
it takes slightly more than two seconds
to uniformly slow down to a stop.
Let's define part one as
when the turntable is uniformly speeding up.
Part two is when the turntable is moving
at a constant angular velocity.
And part three is when the turntable is
uniformly slowing down.
Billy, please describe what you see
when we add the tangential velocity vectors to the picture.
- [Billy] Okay, um, during part one,
the tangential velocities of the mints look like
they are increasing in magnitude.
During part two, the tangential velocities
of the mints are constant in magnitude.
And during part three, the tangential velocities
of the mints seem to be decreasing in magnitude.
Uh, this must be because the tangential velocity equals
radius times angular velocity.
And, in part one, the angular velocity is increasing.
During part two, the angular velocity is constant.
And during part three, the angular velocity is decreasing.
Oh, and the tangential velocities are directly proportional
to the radii.
In other words, the mints, which have a larger path radius
have a larger tangential velocity.
- [Mr. P] Very nice, Billy.
Now, let's remove the tangential velocities
and add tangential acceleration vectors.
Bo, please describe what you see when you look
at the tangential acceleration vectors.
- [Bo] Well, um, during part one,
each mint has a tangential acceleration
with a constant magnitude.
During part two, the tangential accelerations are all zero.
And during part three,
each mint has a tangential acceleration,
which has a constant magnitude and is opposite
in direction to what it was in part one.
Um, and their magnitudes are smaller.
Um, this is because tangential acceleration
equals radius times angular acceleration
and, during parts one and three,
the angular accelerations are opposite in direction
and, during part three,
the angular acceleration is less than what it is
in part one.
Um, and, during part two, the angular acceleration
of the turntable is zero.
Oh, and just like the tangential velocities,
the tangential accelerations are directly proportional
to the radius of the path, which means the larger the radius
of the path of the mint, the larger the magnitude
of the mint's tangential acceleration.
- [Mr. P] Well done, Bo.
Now, let's put all three parts on the screen,
at the same time, with the vectors for tangential velocity
and tangential acceleration simultaneously.
And, Bobby, could you please summarize what we see?
- [Bobby] Sure, uh, looking at part one,
the angular velocity is increasing,
which means the tangential velocities are increasing
in magnitude.
Uh, there is a constant angular acceleration,
so the tangential accelerations have a constant magnitude.
Um, looking at part two, the angular velocity is constant,
which means the tangential velocities
have a constant magnitude.
The angular acceleration is zero;
therefore, there is zero tangential acceleration.
Uh, looking at part three,
the angular velocity is decreasing,
which means the magnitudes
of the tangential velocities are decreasing.
The angular acceleration is constant
and opposite the direction in part one;
therefore, the magnitudes
of the tangential accelerations are constant
and opposite the directions they were in part one.
- [Mr. P] Absolutely, Bobby.
So, notice, just like we talked about before,
with a bicycle, when an object is speeding up,
the velocity and acceleration are in the same direction
and, when an object is slowing down,
the velocity and acceleration are in opposite directions.
Now, let's go back to just one turntable.
Please be aware that angular displacement,
angular velocity, and angular acceleration refer
to the whole object.
Whereas, arc length, tangential velocity,
and tangential acceleration refer to specific parts
of or locations on an object,
which is why we can describe the angular velocity
of the whole turntable; however, when we refer
to tangential velocity, we have to refer
to the tangential velocity of a specific point
on the object.
For example, we cannot say the tangential velocity
of the whole turntable equals any specific value,
because the whole turntable does not have
a specific tangential velocity.
Only specific radii
on the turntable have specific tangential velocities.
- That makes sense. - Sure, yeah.
- Oh, okay. - Thanks.
- Thank you very much for learning with me today.
I enjoyed learning with you.