Monday, November 26, 2012

How Cats Always Fall on their Feet

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.
Cats can also land safely because it has been said that they do not have a deadly terminal velocity. To figure out what the terminal velocity of a cat is, all the forces acting on the cat must be equal to zero.

m=4.5 kg
r=.125 m

Fd= ½ Cd ρ A v2
mg=½ Cd ρ A vmax2
(4.5 kg)(9.8 m/s2)=1/2 (0.4)(π*(.125m)2)(1.2754 kg/m3)(v2)
v=60 m/s

The moment of inertia of a cat with its legs extended would be (assumed to be a cylinder):
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

This shows how if angular momentum is kept constant, this change in moment of inertia can have a big effect on angular speed.

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