Moment of inertia of a merry-go-round

Click For Summary
SUMMARY

The moment of inertia of a merry-go-round is correctly calculated using the formula I = MR², which represents the rotational inertia of a hoop about its central axis. This choice is justified as the mass of the merry-go-round is primarily concentrated at the outer edge, resembling a hoop rather than a disk. The confusion arises from the lack of explicit information regarding the mass distribution in the problem statement. The discussion highlights the importance of understanding the physical configuration of objects when applying rotational inertia formulas.

PREREQUISITES
  • Understanding of rotational inertia concepts
  • Familiarity with the formulas I = (1/2)MR² and I = MR²
  • Basic knowledge of mass distribution in physical objects
  • Awareness of playground equipment and its physics implications
NEXT STEPS
  • Research the differences between the moment of inertia for disks and hoops
  • Explore real-world applications of rotational inertia in playground equipment design
  • Study the physics of rotational motion and angular momentum
  • Investigate safety standards and historical changes in playground equipment
USEFUL FOR

Physics students, educators, mechanical engineers, and anyone interested in the principles of rotational motion and playground equipment design.

brendan3eb
Messages
53
Reaction score
0
In a certain problem I was working on, it asks for the inertia of a merry-go-round, and my first instinct was that it would be the inertia of a disk about its central axis I=(1/2)MR^2, but the solution actually uses I = MR^2 the rotational inertia of a hoop about the central axis. Why do they choose the hoop and not the disk? There is nothing mentioned about how the mass is spread out, just that there is a merry-go-round.
 
Physics news on Phys.org
The merry-go-round I picture have horses around the outer edge that the kids (or bigger kids!) sit on, so most of the mass is at the outer edge - hence a hoop.
It is a bit unfairly worded as a question though.
 
ahhh, yeah, see it said a merry-go-round at a playground so I was thinking of that thing where there are just bars extending from the center and you have to hold on as it spins really fast. I don't know what it is called but I thinked that they stopped making them for safety reasons. Those things were sweet and great examples of basic physics concepts.

Anyway, thanks for pointing that out. It makes more sense now.
 

Similar threads

Moment of inertia of a disk about an axis not passing through its CoM
  • · Replies 11 ·
Replies
11
Views
3K
Rotational Inertia: Hoop vs Disk
  • · Replies 19 ·
Replies
19
Views
4K
Angular momentum changing as mass moves to center
  • · Replies 2 ·
Replies
2
Views
2K
How Does Angular Momentum Remain Conserved in a Merry-Go-Round System?
  • · Replies 8 ·
Replies
8
Views
2K
What is the "r" in the moment of inertia?
  • · Replies 13 ·
Replies
13
Views
3K
Parallel Axis Theorem Not Working
  • · Replies 28 ·
Replies
28
Views
2K
Correct Use of the Parallel Axis Theorem for Moment of Inertia
  • · Replies 2 ·
Replies
2
Views
2K
Moment of inertia of a cuboid parallel to one of its faces (repost with diagram)
  • · Replies 25 ·
Replies
25
Views
2K
Calculating Moment of Inertia for Hollow Cylinder w/ Water
  • · Replies 40 ·
2
Replies
40
Views
6K
Moment of inertia of T bar about 3 axes
  • · Replies 21 ·
Replies
21
Views
2K