Penny Drop Stick
L/2
x
h

mg
  mg
1
2
   t2 
h  x sin 

Free fall drop:
L
I
2
m gL 2
t
4I
3g 2
t
4L
h 
 h  h if


3g 2
t
4L
for small 
1 2
gt
2
2
x L
3

I
m gL
2I
1
m L2
3
Hinged Stick and Ball

L
3g 2
t
4L
t  time for cup to fall
(along arc)
H
H  L sin  
1
g T2
2
T  time for ball to fall
(straight down)

x
 T > t if
2L
4L
sin  

g
3g
2
sin   
3
which is satisfied for all  < c , where
c  1.496  85.7