Why Won't a Disk Rotate on a Frictionless Bearing?

In summary, the conversation discusses the inability to rotate a disk when mounted to a frictionless bearing due to the absence of friction. The use of the parallel axis theorem is mentioned to calculate the moment of inertia of the disk, and it is clarified that Mg does not cause the disk to rotate due to its lack of torque. The question is raised about whether the force of Mg provides any torque about the disk's center, which can affect the rotation rate of the disk.
  • #1
Lil123
8
0
Homework Statement
Find the period of a pendulum consisting of a disk of mass M and radius R fixed to the end of a rod of length l and mass m. How does the period change if the disk is mounted to the rod by a frictionless bearing so that it is perfectly free to spin?
Relevant Equations
T=2pi/ omega
I was able to solve first part I.e. time period of the system when bearing has friction I am unable to figure it out why disk will not rotate when it is mounted to frictionless bearing ?

I know that due to absence of friction disk cannot rotate but then Mg is also there which can rotate the disk about pivoted point
Screenshot_20230610-141227_Drive.jpg
 
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  • #2
You understand that when the disc is mounted to a frictionless axle that it maintains the same orientation as it swings back and forth, right?

Can you show us your work when you did the calculations for the first part? Did you use the parallel axis theorem?
 
  • #3
jbriggs444 said:
You understand that when the disc is mounted to a frictionless axle that it maintains the same orientation as it swings back and forth, right?

Can you show us your work when you did the calculations for the first part? Did you use the parallel axis theorem?
20230613_154202.jpg
yes , I did used parallel axis theorem to find moment of inertia of disk about pivoted point
 
  • #4
Lil123 said:
Mg is also there which can rotate the disk about pivoted point
The mass centre of the disc is either at the pivot point or hangs directly below it. Either way, Mg has no torque about the pivot, so will not cause the disc to rotate.
 
  • #5
Can you explain more clearly please
 
  • #6
Lil123 said:
Can you explain more clearly please
As to the point being made by @haruspex, the rotation rate of the disc about its own center can vary if there is a torque about the disc's center. Does the force from ##mg## acting on the disc provide any torque about the disc's center?

If not, why would the disc ever rotate about its own center?
 
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FAQ: Why Won't a Disk Rotate on a Frictionless Bearing?

Why won't a disk rotate on a frictionless bearing?

A disk won't rotate on a frictionless bearing because there is no external torque applied to initiate or maintain the rotation. Frictionless bearings eliminate resistance, but they also mean that no force is acting to start the motion.

Can a disk start rotating on its own on a frictionless bearing?

No, a disk cannot start rotating on its own on a frictionless bearing. Without an external force or torque, the disk will remain in its initial state of rest due to Newton's First Law of Motion.

What role does friction play in the rotation of a disk?

Friction provides the necessary force to initiate and maintain the rotation of a disk. It acts at the point of contact between the disk and the surface, allowing the transfer of torque that causes the disk to spin.

How can you make a disk rotate on a frictionless bearing?

To make a disk rotate on a frictionless bearing, you need to apply an external torque or force. This can be done using a motor, a push, or any other method that introduces a rotational force to the disk.

Is perpetual motion possible with a frictionless bearing?

No, perpetual motion is not possible even with a frictionless bearing. While frictionless bearings reduce resistance, other factors like air resistance and material imperfections will eventually slow down and stop the motion. Additionally, the laws of thermodynamics prohibit perpetual motion.

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