Mass Moments
For the point mass figure below, what is the mass moment of inertia?
Expand Hint
For point masses, the mass moment of inertia is:
$$$I=\sum m_ir_i^2$$$
where
$$m$$
is the mass, and
$$r$$
is the perpendicular distance to the rotation axis.
Hint 2
Ignore the 1.75 m and 1 m distances. Those dimensions are there to throw you off.
For point masses, the mass moment of inertia is:
$$$I=\sum m_ir_i^2$$$
where
$$m$$
is the mass, and
$$r$$
is the perpendicular distance to the rotation axis.
The figure has four point masses:
$$$I=m_1r_{1}^{2}+m_2r_{2}^{2}+m_3r_{3}^{2}+m_4r_{4}^{2}$$$
Remember,
$$r$$
is the perpendicular distance the mass is from the rotation axis, not parallel distance, meaning the 1.75 m and 1 m dimensions are there for confusion and can be ignored. Starting from the bottom right point mass and moving clockwise:
$$$I=(0.25kg)(0.2m)^{2}+(0.25kg)(0.2m)^{2}+(0.65kg)(0.2m)^{2}+(0.25kg)(0.2m)^{2}$$$
$$$=(0.04m^{2})[0.25kg+0.25kg+0.65kg+0.25kg]=0.056\:kg\cdot m^2$$$
$$$0.056\:kg\cdot m^2$$$
Time Analysis
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