```Tjcondit1

Q: given angular velocity, time and radius how to you figure distance
along the perimeter?

To find a distance we need a rate (speed) multiplied by a time.

The tangential speed is given by the angular velocity times the radius

(1)      v = wr

where w = angular velocity

The distance along a perimeter (of a circle) is the tangential speed times
time.

(2)    d = vt

where d = the distance along the perimeter
v = the tangential velocity defined in (1) above
t = time

Substituting for v from (1) in the formula for distance (2) gives
*************
(3)          *  d = wrt  *
*************

Note: If the angular velocity is in degrees per second first multiply by
pi (3.14159...)
and divide by 360 to convert w to radians per unit time.

Note: if w is not constant then the above is not true. We must replace wt
in formula (3)
with an intrgral over time from 0 to t.
/
d = r| w dt
/

Q: given the straight line velocity, time and radius how to you figure
distance along the perimeter?

I will assume that you mean the tangential velocity when you say straight
line velocity.
In this case distance is just the straight line velocity times the time
not needed!

d = vt

Where d = distance
v = tangential velocity
t = time.

If v is variable with time then you have to do an integral.

/
d =  | v dt
/

note: When text books speak of velocity they usualy mean a vector quantity
but in the context of uniform circular motion they are usualy
talking

note: I am a little suspicious about the wording of this question. I
wonder
if what you really are asking about is angle?  If so the you can get
the
angular velocity w by dividing v by r

w = v/r

the angle in radians swept out by an object moving along a circle
will be

angle = wt

where t is time. Substituting v/r for w in the above equation then
gives

angle = (v/r)t

```