## A Robotic Arm

Imagine a 40 cm long robotic arm that rotates around to serve you a coffee. If it weighs 80 N, what is the mass moment of inertia?

##
__
__**Hint**

**Hint**

Because the arm rotates/gyrates around, we can use the radius of gyration formula:

$$$r_{m}=\sqrt{\frac{I}{m}}$$$

where
$$r$$
is the distance from a reference axis,
$$I$$
is the mass moment of inertia, and
$$m$$
is the mass.

##
__
__**Hint 2**

**Hint 2**

$$$Force=mass \times acceleration$$$

$$$Force=mass \times acceleration$$$

Solving for mass:

$$$m=\frac{F}{a}=\frac{80N}{9.8m/s^2}=8.16\:kg$$$

Because the arm rotates/gyrates around, we can use the radius of gyration formula:

$$$r_{m}=\sqrt{\frac{I}{m}}\rightarrow I=m\cdot r^{2}$$$

where
$$r$$
is the distance from a reference axis,
$$I$$
is the mass moment of inertia, and
$$m$$
is the mass. Thus,

$$$I=8.16kg\cdot (40cm)^2=13,061 \:kg\cdot cm^2$$$

$$$13,061 \:kg\cdot cm^2$$$