By Siyun Zou

Fear
factor is an American reality game show where a bunch of contestants compete
against one another performing dangerous stunts for $50,000. The rotating
platform escape is one of the most interesting stunts.

Total moment of Inertia:

Total mass= 60kg

L=2.74 m

W= 1.22 m

I= 1/12 M (L

^{2}+W^{2})
I= 1/12 (60kg)(2.74

^{2}+1.22^{2})__I= 45 kgm__

^{2}
Estimated rotational Velocity of the spinning
platform from video: 1 revolution per 16s

f = 0.0625 rev/sec

ω = 2πf= 2π(0.0625rev/sec)=

__0.393 rad/s__
The contestant took approximately 40s to set herself free
from the rotating platform

ω

_{f}= ω_{i}+ αt^{2}
0.393 rad/s= 0 + α (40s)

^{2}__α = 2.26E-4 rad/s__

^{2}
Calculation of her buoyant force when she is completely
submerged:

Average swimming pool volume= 375m

^{3}
Volume of the platform = (2.74m*1.22m*0.508) = 1.70 m

^{3}
F

_{B}= ρVg = 1.70 m^{3}(9.8m/s^{2}) (1000 kg/m^{3})__F__

_{B}__= 16660 N__

∑F= F

_{B}-F_{g }
∑F= Vg (ρ

_{f}– ρ_{i}) -ma
∑F=16660 N-
(60kg*9.8m/s

^{2})__∑F=1.6E4 N__

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