A Robotic Arm
Imagine a 40 cm long robotic arm that rotates around to serve a cup of coffee. If it weighs 80 N, what is the mass moment of inertia in kg∙cm^2?
Expand Hint
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.
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, 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. Thus,
$$$I=8.16kg\cdot (40cm)^2=13,061 \:kg\cdot cm^2$$$
$$$13,061 \:kg\cdot cm^2$$$
Time Analysis
See how quickly you looked at the hint, solution, and answer. This is important for making sure you will finish the FE Exam in time.- Hint: Not clicked
- Solution: Not clicked
- Answer: Not clicked
Similar Problems from FE Sub Section: Mass Moment of Inertia
331. Mass Moment of Inertia
334. Mass Moments
631. Robotic Arm
Similar Problems from FE Section: Plane Motion of a Rigid Body
330. Figure Skating
331. Mass Moment of Inertia
334. Mass Moments
631. Robotic Arm