By Danielle LaPaglia
Whenever cats fall, they are almost always able to orient
themselves so that they land on their feet. They are able to do this because
they have a very flexible spine and can rotate the front half of their body
separately from the back half. First, the cat tucks in its front legs to rotate
the front half of its body quickly. This works because it decreases its moment
of inertia and causes angular velocity to increase. Then, the cat stretches out
its front legs and tucks in its back legs so that the back half of its body can
follow suit. The cat is then in position to land feet first on the ground. The
conservation of angular momentum (L=Iω) allows the relationship between
moment of inertia and angular velocity to be true. No external forces are
acting on the cat when it is falling, therefore its momentum will be constant.

Assumptions:
m=4.5 kg
C_{d}=0.4
r=.125 m
F_{d}= ½ C_{d} ρ A
v^{2}
F_{g}=mg
mg=½ C_{d} ρ A v_{max}^{2}
(4.5 kg)(9.8 m/s^{2})=1/2 (0.4)(π*(.125m)^{2})(1.2754
kg/m^{3})(v^{2})
v=60 m/s
The moment of inertia of a cat with its legs extended would
be (assumed to be a cylinder):
I=1/2mr^{2}
I=1/2(4.5 kg)(.0625m)^{2}
I=.0087 kg m/s
As opposed to having it’s legs tucked in (r increases):
I=1/2(4.5 kg)(.125 m)^{2}
I=.035 kg m/s
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