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

[Lil123]

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

 

[jbriggs444]

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?

 

[Lil123]

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?

yes , I did used parallel axis theorem to find moment of inertia of disk about pivoted point

 

[haruspex]

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.

 

[Lil123]

Can you explain more clearly please

 

[jbriggs444]

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?