Angular Position Post-Lab
s m 
C
A
B
B
C
A
r m 
Since each graph is
linear and contains (0,0)
sr

For a particular
reference line
s  ##m
r m

Notice that every reference line has
its own slope, and that the farther
the reference line is from 0 the
steeper the slope.
Angular Position Post-Lab
Angular Position   - the slope of a graph
of arc length vs radius
s  r
s

r
Notice that the angular position is
dimensionless, it is a pure number.
However, while the angular position is
dimensionless it is not without units!.
Angular Position Post-Lab
Angular Position   - the slope of a graph
of arc length vs radius
s  r
radians rad   the ratio of the arc length to the radius
 the angle subtended by a circular arc
s

r
Arc Length = Radius
Arc Length
1 rad
Radius
 An angle whose two rays pass through 


 the endpoints of the arc

1 rad = the angular position resulting in an arc
length and a radius of equal length
Angular Position Post-Lab
Angular Position   - the slope of a graph
of arc length vs radius
s  r
s

r
Radian measure
radians rad   the ratio of the arc length to the radius
 the angle subtended by a circular arc
Radian measure
For a full revolution:
 An angle whose two rays pass through 


 the endpoints of the arc

s 2 r
 
 2 rad
r
r
2 rad  360  1 rev revolution 
Angular Position Post-Lab
s m 
Check out the angular position of
reference line B
C
B
Slopes
A
Since reference line B is half way
around
r m 
A
B
0
C
s r
B  
  rad
r
r
What are the angular positions of
reference lines A and C in degrees?
360
 A  0.52 rad 
 30
2 rad
360
C  4.2 rad 
 240
2 rad
Rolling
Consider a disk rolling without slipping at a constant velocity.
While most points both rotate and move linearly, the center
 of mass is only moving
linearly with a constant speed vcm

vcm
Rolling
Both a point on the outside of the
disk and the center of mass must
move a distance s for the disk to
roll without slipping!
s  R
Rolling Condition – must hold for
an object to roll without
slipping.
R
s
s


vcm