Compute the moment of inertia of your body as you stand tall and turn around a vertical axis passing through the top of your head and the point halfway between your ankles. Model your body as a cylinder of mass 59.5 kg and circumference 84.5 cm.
I got the answer to be 10.6 by multiplying 59.5 by .4225m^2 but it's saying my answer's too small...
I= 1/2 m r^2=1/2 59.5 * (.845/2PI)^2
I am not certain how you got r to be .4225, but even at that, you did not square it.
To calculate the moment of inertia of your body as described, we need to use the formula for the moment of inertia of a cylindrical object, which is given by:
I = (1/2) * m * r^2
Where:
I = the moment of inertia
m = mass of the object
r = radius of the object
Given that your body is modeled as a cylinder with a mass of 59.5 kg and a circumference of 84.5 cm, let's calculate the radius first. The circumference (C) of a circle is related to its radius (r) by the formula: C = 2 * π * r
Since the circumference is given as 84.5 cm, we can rearrange the formula to solve for the radius:
r = C / (2 * π)
Plugging in the given value:
r = 84.5 cm / (2 * π) = 13.472 cm
Now, we need to convert the radius from centimeters to meters:
r = 13.472 cm * (1 m / 100 cm) = 0.13472 m
Using this value of the radius, we can calculate the moment of inertia:
I = (1/2) * 59.5 kg * (0.13472 m)^2
I = 0.120955 kg*m^2
Therefore, the moment of inertia of your body as you stand tall and turn around the described axis is approximately 0.121 kg*m^2, which is different from the answer you obtained.
It seems like you made a calculation error while squaring the radius. When you squared 0.13472 m, you should have obtained approximately 0.018162 m^2, not 0.4225 m^2. Correcting that mistake should give the correct answer.