Modelling the Tea-Cup Ride
In this activity you will use the construction and transformation facilities to model the
Tea-cup fairground ride. Then explore the locus of person sitting in a cup for different
platform and cup size, and different relative speeds.
Sketch and Investigate
Select the line
segment tool to
construct two
segments.
1. Construct line segments AB (radius/distance to centre of cup on the
platform, which we will call platform radius) and CD (radius of cup)
A
Ron Sketchpad notes/Teacup ride by transformations
B
C
D
Select point tool
to create a point.
Highlight (click
to select) AB and
E in then in
Construct menu
choose Circle By
Centre + Radius
to create circle
centre E
(platform)
Place a point F on
this circle and
similarly create
circle centre F
(cup)
2. Construct circle centre E (platform) and circle centre F (cup).
First create new
parameter
platformangle In
the Measure
menu choose
Calculate then
New Parameter.
Edit as opposite.
3. To simulate platform rotation construct point (person) on the cup and rotate
cup etc. about E through some platformangle (say 30º)..
F
E
Highlight
platformangle,
right click mouse
and choose Mark
angle.
Double click on E
to mark as
Centre of
Rotation
In the Transform
menu choose
Rotate. This will
produce rotate
window opposite
(with marked
angle selected).
Click Rotate.
Ron Sketchpad notes/Teacup ride by transformations
B
A
platformangle = 30.00
person'
C
D
F'
person
F
E
Double
platformangle In
the
Measure menu,
choose
Calculate.
Use the mouse to
select
platformangle
then on the
calculator
keyboard “*” and
“2” Click OK and
mark this angle as
in 3.
4. The cup can also rotate about its own pivot F (or F’) We will assume that it
rotates about F (F’) at twice the rate of the platform to produce the second
transformed image person”
Ron Sketchpad notes/Teacup ride by transformations
platformangle = 30.00
platformangle2 = 60.00
B
A
person'
person''
C
D
F'
person
F
E
Highlight point
person”. In the
Display menu
choose Trace
Point.
Highlight
platformangle
and right click the
mouse and
choose animate
parameter.
5. We can now simulate the ride by varying the platform angle through the
animation facility and tracing person”.
6. The original cups, centre F etc. can be hidden.
Explore changing the platform and cup sizes, and relative rates of rotation.
Try to visualise the locus of a person in the ride with a cup radius of half
platform radius and equal rates of rotation (i.e calculated angle
platformangle*2 becomes just platformangle).
How would you edit the parameters so that the cup rotates in the opposite
direction to the platform?
Ron Sketchpad notes/Teacup ride by transformations
Ron Sketchpad notes/Teacup ride by transformations