Question

Olga, the 50.0-kg gymnast, swings her 1.6-m-long body around a bar by her outstreched arms. A.) what is olga's moment of inertia? B.) If olga were to pull in her legs thereby cutting her body length in half, how would this change her moment of inertia?

Answer 1

A) 42.7 kg m^2

We can consider Olga has a uniform rod, rotating about one of her end, with her mass distributed along the body. Therefore, her moment of inertia is given by

`I=(1)/(3)mL^2`

where

m = 50.0 kg is the mass

L = 1.6 m is the length of Olga's body

Substituting into the equation, we find

`I=(1)/(3)(50.0 kg)(1.6 m)^2=42.7 kg m^2`

B) 10.6 kg m^2

The problem is the same as before, however this time the length of Olga's body is just half the length she had before:

`L=(1.6 m)/(2)=0.8 m`

Therefore, her moment of inertia will be

`I=(1)/(3)(50.0 kg)(0.8 m)^2=10.6 kg m^2`