0
$\begingroup$

enter image description here

In this system moment of inertia of the whole system about the axis shown in the question is given ( sphere is able to freely rotate about its axis)

"i want to know why we are not treating sphere as a point mass? why are we considering its rotation about its own axis and adding its moment of inertia *as all the points of the sphere are moving in the same way around the axis * .i am not able to see any rotational motion of sphere about its axis so why are we considering its moment of inertia about its axis

But according to me Moment of inertia of this system should be like this. treating sphere as point mass located at L+R distance from the axis of rotation enter image description here

Improve this question
$\endgroup$
6
  • $\begingroup$ Perhaps you might want to revisit the question. The question might have explicit statement saying that the sphere can freely rotate about an axis, very likely the rod would extent as an axis and the sphere could rotate about this axis. $\endgroup$
    – TheImperfectCrazy
    Mar 9, 2021 at 11:22
  • 1
    $\begingroup$ Why do you think that the spheres should be point masses? They have a nonzero radius, besides if they were point masses your handwritten expression would still be incorrect, as the last term wouldn't have $(L+R)^2$. $\endgroup$
    – Triatticus
    Mar 9, 2021 at 11:23
  • $\begingroup$ because all the point of the sphere are moving in the same way around the axis and the last term would be correct beacuse if we treat it as a point mass than all its mass can be assumed at its geometrical center which is at a distance (L+R) from the axis of rotation $\endgroup$
    – Samardeep singh
    Mar 9, 2021 at 11:31
  • $\begingroup$ i am not able to see any rotational motion of the sphere about its axis so why are we considering its moment of inertia about its axis $\endgroup$
    – Samardeep singh
    Mar 9, 2021 at 11:46
  • $\begingroup$ All points of the sphere are "moving the same way around the axis", but the points do not all have the same radius from the axis. But the sphere is rotating in the same way the Earth's moon is rotating. $\endgroup$
    – garyp
    Mar 9, 2021 at 11:47

1 Answer 1

Reset to default
1
$\begingroup$

OP - Why we are not considering the sphere as point mass?

As it's not a point mass. The sphere has a distribution of mass in a finite space that we have to consider. The moment of inertia of the sphere is different than the point mass. If you take a point on a sphere then its distance from the axis of rotation will change as you move the point around the surface of the sphere.

In the limit when $L>>R$, Then you might ignore the distribution of mass and can consider the sphere as a point mass. That is reflected from the fact $$\lim_{L\rightarrow \infty} I_{\text{on image}}=I_{\text{by OP}}$$

Improve this answer
$\endgroup$
2
  • $\begingroup$ can you also tell me if we see it in the frame of sphere will the sphere rotate about its axis $\endgroup$
    – Samardeep singh
    Mar 9, 2021 at 13:10
  • $\begingroup$ Consider the point where the sphere is attached to the rod. In your sketch it is on the left side of the sphere. Half a revolution later it is on the right. It is rotating at the same rate as the rod. $\endgroup$
    – R.W. Bird
    Mar 9, 2021 at 15:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.