Good morning.
Bo, remind me. What does UAM stand for?
♫ Flipping Physics ♫
Bo: UAM means "Uniformly Accelerated Motion."
Just like an object can have uniformly accelerated motion, an object can also have uniformly angularly accelerated motion.
Because "uniformly angularly accelerated motion" is difficult to say, I usually call it "U fishy M."
Billy: U fishy M!
Bo: U fishy M? Ucch!
Mr. P: In order to extend our understanding of UAM to UαM, let's review UAM briefly.
Billy, when can we use the UAM equations?
Billy: We can use the uniformly accelerated motion equations
if the acceleration of the object is constant; that's what it means to be uniform.
Bobby: In other words, the acceleration equals a number.
Mr. P: Correct.
Class, there are how many UAM variables?
Five.
There are how many UAM equations?
Four.
If we know how many of the UAM variables:
Three.
We can find the other:
Two.
Which leaves us with one:
Happy Physics Student!
UAM is linear. UαM is angular.
Bobby, when can we use the uniformly angularly accelerated motion equations?
Bobby: We can use the UαM equations when...
the angular acceleration of the object is constant, meaning "fishy thing" equals a number.
Mr. P: There are five variables in uniformly accelerated motion. They are:
velocity final, velocity initial, acceleration, displacement, and change in time.
Bo, just like there are five UAM variables, there are five UαM variables. What are they?
Bo: Well, looking at the linear UAM variables, the angular U alpha M variables...
Billy: You mean, "fishy thing."
must be...
angular velocity final, angular velocity initial, angular acceleration, angular displacement, and change in time.
Mr. P: Bobby, please determine the first of the UαM equations.
Bobby: Well, uh, looking at the first UAM equation, the first UαM equation must be:
angular velocity final equals angular velocity initial plus angular acceleration times change in time.
Mr. P: And Billy, what about the other three uniformly angularly accelerated motion equations?
Billy: The second UαM equation is:
change in angular position equals
angular velocity initial times change in time plus 1/2 angular acceleration times change in time squared.
The third one is:
angular velocity final squared equals angular velocity initial squared
plus 2 times angular acceleration times change in angular position,
and the fourth one is:
change in angular position equals 1/2 times the quantity (angular velocity final plus angular velocity initial),
all times change in time!
Mr. P: Which means, class, there are how many UαM variables?
Five.
There are how many UαM equations?
Four.
And if we know how many of the UαM variables:
Three.
We can figure out the other:
Two.
Which leaves us with one:
Happy Physics Student!
That is because the UαM equations work just like the UAM equations.
OK, a few more things to make sure you are aware of.
When you use the uniformly angularly accelerated motion equations, please use radians for your angular quantities.
Most of the time, you have to use radians in the UαM equations,
and you always can use radians in the UαM equations, therefore:
Please, I suggest you always use radians in the UαM equations.
Also, every example I gave in a previous video of objects with angular acceleration
actually have a constant angular acceleration.
So each of these is an example of an object turning with uniformly angularly accelerated motion, or UαM.
Let's also take a moment to discuss the difference between average angular velocity
and the angular velocities in the UαM equations.
Average angular velocity equals
change in angular position over change in time.
How are the angular velocities in the UαM equations
different than the average angular velocity?
Bobby: All of the angular velocities in the UαM equations are initial or final angular velocities,
so they are instantaneous angular velocities, uh, they are at a specific time,
which is different than the average angular velocity equation you just drew on the board, which is over a time period.
Billy: Well, blimey!
You know what, I just noticed that that last UαM equation
is a rearranged version of the equations for average angular velocity.
Average angular velocity equals angular displacement over change in time,
and when the angular acceleration is constant, like it is in uniformly angularly accelerated motion,
it also equals angular velocity final plus angular velocity initial, all divided by 2.
Move the change in time to the other side, and you have the last of the UαM equations, and that is aces!
Mr. P: And lastly, one of the biggest hurdles for students when learning about circular motion is all of the new symbols and terms,
which means you should be saying what all the variables mean as you work with them.
This will help you to not only remember the new variables, but to also remember what the variables mean.
Thank you very much for learning with me today; I enjoyed learning with you.