Question

Estimate the rotational inertia for a person rotating around a vertical axis passing through their center of mass wile in a "t-pose" position, as shown below. Use simplified shapes for the head, arms, legs, and torso. Use the table below (which is also in your book) for the moments of inertia for simple shapes. Use the parallel axis theorem where appropriate. Don't forget to list all your estimates for all relevant variables. Axis R Hoop about cylinder axis Axis Annular cylinder (or ring) about cylinder axis $I = MR^2$ $I = \frac{M}{2}(R_1^2 + R_2^2)$ Axis Axis Solid cylinder (or disk) about cylinder axis Solid cylinder (or disk) about central diameter $I = \frac{MR^2}{2}$ $I = \frac{MR^2}{4} + \frac{MR^2}{12}$ Axis Axis $I = \frac{MR^2}{12}$ Thin rod about axis through center \perp to length $I = \frac{MR^2}{3}$ Thin rod about axis through one end \perp to length Axis Axis Solid sphere 2R about any diameter $I = \frac{2MR^2}{5}$ $I = \frac{2MR^2}{3}$ Thin 2R spherical shell about any diameter Axis R Hoop about any diameter $I = \frac{MR^2}{2}$ Axis Slab about \perp axis through center a $I = \frac{M(a^2 + b^2)}{12}$ b

          Estimate the rotational inertia for a person rotating around a vertical axis passing through their center of mass wile in a
"t-pose" position, as shown below. Use simplified shapes for the head, arms, legs, and torso. Use the table below
(which is also in your book) for the moments of inertia for simple shapes. Use the parallel axis theorem where
appropriate. Don't forget to list all your estimates for all relevant variables.
Axis
R
Hoop about
cylinder axis
Axis
Annular cylinder
(or ring) about
cylinder axis
$I = MR^2$
$I = \frac{M}{2}(R_1^2 + R_2^2)$
Axis
Axis
Solid cylinder
(or disk) about
cylinder axis
Solid cylinder
(or disk) about
central diameter
$I = \frac{MR^2}{2}$
$I = \frac{MR^2}{4} + \frac{MR^2}{12}$
Axis
Axis
$I = \frac{MR^2}{12}$
Thin rod about
axis through
center \perp to
length
$I = \frac{MR^2}{3}$
Thin rod about
axis through one
end \perp to length
Axis
Axis
Solid sphere
2R about any
diameter
$I = \frac{2MR^2}{5}$
$I = \frac{2MR^2}{3}$
Thin
2R spherical shell
about any
diameter
Axis
R
Hoop about
any diameter
$I = \frac{MR^2}{2}$
Axis
Slab about
\perp axis through
center
a
$I = \frac{M(a^2 + b^2)}{12}$
b

Estimate the rotational inertia for a person rotating around a vertical axis passing through their center of mass wile in a
"t-pose" position, as shown below. Use simplified shapes for the head, arms, legs, and torso. Use the table below
(which is also in your book) for the moments of inertia for simple shapes. Use the parallel axis theorem where
appropriate. Don't forget to list all your estimates for all relevant variables.
Axis
R
Hoop about
cylinder axis
Axis
Annular cylinder
(or ring) about
cylinder axis
I = MR^2
I = (M)/(2)(R1^2 + R2^2)
Axis
Axis
Solid cylinder
(or disk) about
cylinder axis
Solid cylinder
(or disk) about
central diameter
I = (MR^2)/(2)
I = (MR^2)/(4) + (MR^2)/(12)
Axis
Axis
I = (MR^2)/(12)
Thin rod about
axis through
center ⊥to
length
I = (MR^2)/(3)
Thin rod about
axis through one
end ⊥to length
Axis
Axis
Solid sphere
2R about any
diameter
I = (2MR^2)/(5)
I = (2MR^2)/(3)
Thin
2R spherical shell
about any
diameter
Axis
R
Hoop about
any diameter
I = (MR^2)/(2)
Axis
Slab about
⊥axis through
center
a
I = (M(a^2 + b^2))/(12)
b

Added by James H.

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