Bo: Hey, Guys.
Billy: Hey, Bo.
Bobby: Hi, Bo.
♫ (lyrics) Flipping Physics ♫
Mr. P: Ladies and Gentlepeople, the bell has rung,
therefore class has begun, therefore,
you should be seated in your seat, ready and excited
to review mechanics dimensions because dimensions are your?
Billy, Bobby and Bo: Friends.
Mr. P: Great, dimensions are your friends.
Billy, what are the dimensions for force?
Billy: Force is in newtons.
Mr. P: Bobby, what is the symbol for arc length?
Bobby: The symbol for arc length is a lowercase s.
Mr. P: Yes, I use a lowercase cursive s
for my arc length because my s's are so terrible.
Bo, what are the dimensions for arc length?
Bo: Arc length is in meters.
Mr. P: Bobby, what are the dimensions
for tangential velocity?
Bobby: Tangential velocity is in meters per second.
Mr. P: Billy, what are the dimensions
for tangential acceleration?
Billy: Tangential acceleration
is in meters per second squared.
Mr. P: Bo, what are the dimensions
for centripetal acceleration?
Bo: Don't centripetal and tangential accelerations
have the same dimensions, meters per second squared?
Mr. P: Yes, you are correct.
Billy, if tangential acceleration
centripetal acceleration both have
the same dimensions, how are they different?
Bobby: Tangential acceleration is tangent to the circle,
while centripetal acceleration is always inward,
so they are 90 degrees to one another.
Bo: Also, you can't have circular motion
without centripetal acceleration.
However, if the angular velocity is constant,
then the angular acceleration is zero
and the tangential acceleration is also zero.
Therefore, while you can't have circular motion
without centripetal acceleration, you can have
circular motion without tangential acceleration.
Mr. P: Very nice.
Bobby, what are the dimensions for work?
Bobby: Work is in joules.
Mr. P: Billy, what else is in joules?
Billy: Kinetic energy, elastic potential energy,
and gravitational potential energy.
All of those are in joules.
Mr. P: Bo, what are the dimensions for power?
Bo: Power is in watts.
Mr. P: Bobby, what is a watt?
Bobby: A watt is a joule per second and a joule
is a newton meter and a newton
is a kilogram meter per second squared.
Mr. P: Very nice, Bobby.
Bo, what are the symbol and dimensions for impulse?
Bo: The symbol for impulse is an uppercase J
and its dimensions are newton seconds
which is the same thing as kilogram meters per second.
Billy: Also, change in momentum is equal to impulse
and therefore also has the same dimensions as impulse.
Oh, and the symbol for momentum is a lowercase p.
Bobby: Not to be confused with uppercase P,
which is power, or rho, which looks like
a curly lowercase p, which is volumetric mass density.
Mr. P: Very nice, you guys have learned well.
Bobby, what are the symbol and
dimensions for angular velocity?
Bobby: The symbol for angular velocity is omega,
which looks like a curly w and it's in radians per second
although it could be in revolutions per minute, however,
usually in physics, we work with it in radians per second.
Mr. P: Billy, what are the symbol
and dimensions for angular acceleration?
Billy: The symbol for angular acceleration is alpha,
or fishy thing, and its dimensions
are radians per second squared.
Mr. P: Bo, what are the symbol and dimensions for torque?
Bo: The symbol for torque is a lowercase tau
and torque is in newton meters, which is, in fact,
a joule, however, we don't call it a joule,
just to distinguish torque from work and energy
and, perhaps, remind us that torque is a vector,
while work and energy are scalars.
Mr. P: Bobby, what are the symbol
and dimensions for linear mass density?
Bobby: The symbol for linear mass density
is lambda and it's in kilograms per meter.
Mr. P: Billy, what are the symbol and
dimensions for moment of inertia?
Billy: The symbol for moment of inertia is
an uppercase I and its dimensions are
kilograms times meters squared.
Mr. P: Bo, what are the symbol and
dimensions for angular momentum?
Bo: The symbol for angular momentum is an uppercase L
and its dimensions are kilograms
times meters squared over seconds.
Mr. P: Very nice, Everybody.
One last time, dimensions are your?
Billy, Bobby and Bo: Friends.
Voiceover: Lecture notes are available
at FlippingPhysics.com.
Please enjoy lecture notes responsibly.
Man falling off swing: Oh, whoa!