I What is the purpose of radius of gyration

AI Thread Summary
The discussion revolves around the confusion regarding the use of radius 'r' and radius of gyration 'Rg' in calculating the moment of inertia for a mass rolling down an incline. It clarifies that the moment of inertia can be expressed as I = mRg^2, where Rg represents the distribution of mass, while I = 1/2 * mr^2 applies specifically to a solid cylinder. Participants question whether the problem specifies the shape of the object, as this affects the appropriate formula to use. The relationship between Rg and r is also discussed, with a suggestion that Rg could be equal to r/√2, depending on the object's characteristics. Understanding the object's geometry is crucial for correctly applying the moment of inertia formula.
TheBlueDot
Messages
16
Reaction score
2
Hello,

I'm given a problem of a mass rolling down an incline with mass 'm', radius 'r', and radius of gyration Rg, and I need to write the Lagrangian for the motion. I'm confused on why both r and Rg are given. Don't I just need one of the two for the moment of inertia?
Thanks!
 
Physics news on Phys.org
The radius of gyration gives the moment of inertia via the equivalence of the given object and an object with all its mass concentrated at a distance of the radius of gyration from the center of mass. So I = m R_g^2.

You can treat the object as a massless cylinder of the given physical radius with a hollow cylinder of mass m and radius R_g embedded within it.
 
Hi jambaugh,

Thank you for your response. The part I'm confused on is if I use Rg the moment of inertia (assume a cylinder) would be I= mRg^2, but if I use 'r', then I=1/2 *mr^2. I guess I don't understand where the question is leading...
 
Why would I = \frac{m}{2} r^2? Is R_g given to be equal to r/\sqrt{2}? Did the problem specifically say the object was a solid disk or cylinder? Maybe the object is not what you are assuming with the \frac{m}{2}r^2 formula.
 
Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »

Thread 'Simple thought experiment with Stefan-Boltzmann law: energy'

Dear all, in an encounter of an infamous claim by Gerlich and Tscheuschner that the Greenhouse effect is inconsistent with the 2nd law of thermodynamics I came to a simple thought experiment which I wanted to share with you to check my understanding and brush up my knowledge. The thought experiment I tried to calculate through is as follows. I have a sphere (1) with radius ##r##, acting like a black body at a temperature of exactly ##T_1 = 500 K##. With Stefan-Boltzmann you can calculate...
View full post »
Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (First part)'

Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (First part)'

I am reading the Griffith, Electrodynamics book, 4th edition, Example 4.8 and stuck at some statements. It's little bit confused. > Example 4.8. Suppose the entire region below the plane ##z=0## in Fig. 4.28 is filled with uniform linear dielectric material of susceptibility ##\chi_e##. Calculate the force on a point charge ##q## situated a distance ##d## above the origin. Solution : The surface bound charge on the ##xy## plane is of opposite sign to ##q##, so the force will be...
View full post »

Similar threads

I Reframing Light Bending Using Density Instead of Radius
Replies
20
Views
636
I A "continous" gravitational field formula r=0 to infinity
Replies
16
Views
679
B Extending the Lagrangian of a double pendulum to more complex systems
Replies
3
Views
1K
I Polymer Physics - Radius of Gyration
Replies
4
Views
5K
I Dimensional analysis in the formula for gyration frequency
Replies
6
Views
1K
I Origin of Centripetal force when the net force toward the center is 0?
Replies
8
Views
3K
I I'm calculating more energy out than I put in
3
Replies
138
Views
8K
I Lagrangian for pendulum
Replies
11
Views
2K
I Problem with understanding angular momentum
Replies
30
Views
3K
I How does the mass of the wheels affect the car's acceleration?
Replies
15
Views
4K

Hot Threads

Recent Insights

Back
Top