Robotic Arm
In a warehouse facility, a robotic arm extends 50 cm to sort items on an assembly line. If the arm’s mass moment of inertia is 20,000 kg∙cm^2, what is its weight in Newtons?
Expand Hint
Because the arm rotates/gyrates around, the radius of gyration formula is applicable:
$$$r_{m}=\sqrt{\frac{I}{m}}\rightarrow I=m\cdot r^{2}$$$
where
$$r$$
is the distance from a reference axis,
$$I$$
is the mass moment of inertia, and
$$m$$
is the mass.
Hint 2
$$$Force=mass \times acceleration$$$
Because the arm rotates/gyrates around, the radius of gyration formula is applicable:
$$$r_{m}=\sqrt{\frac{I}{m}}$$$
where
$$r$$
is the distance from a reference axis,
$$I$$
is the mass moment of inertia, and
$$m$$
is the mass.
$$$50cm=\sqrt{\frac{20,000kg\cdot cm^2}{m}}$$$
$$$(50cm)^2=\frac{20,000kg\cdot cm^2}{m}$$$
$$$m=\frac{20,000kg\cdot cm^2}{2,500cm^2}=8\:kg$$$
Recall:
$$$Force=mass \times acceleration$$$
Thus,
$$$F=8kg \times 9.8\frac{m}{s^2}=78.4\:N$$$
78.4 N
Time Analysis
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