Question

I got a little confused when in the beginning of lecture 6, the professor parametrized the position vector r by using time instead of theta as in the previous lesson.

Before doing that, he stated that (1) the radius would be 1 and (2) unit speed would be used.

So, in order to parametrize the function with time, is it mandatory to make the assumptions (1) and (2)?

What does it really mean to work "at unit speed"?

Thank you in advance,
utxeee.

Answer 1

o, in order to parametrize the function with time, is it mandatory to make the assumptions (1) and (2)?

no, you can use any radius and speed you like, but with r=1 and unit speed, the equations don't have scalars (multipliers).
For example, distance =speed * time
if we set speed=1 , then distance = time
if we set r=1, then the circumference is 2 pi r = 2 pi
and when the circle rolls a distance of 2 pi, it also turns 2 pi radians, so the angle = distance = time.
thus we get especially uncomplicated equations.

Answer 2

phi, thank you :)