Why Does a Disk Begin to Rotate on a Horizontal Surface with Friction?

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Homework Help Overview

The discussion revolves around the mechanics of a uniform disk on a horizontal surface with friction. Participants explore how an applied force can cause the disk to rotate while its center remains at rest, raising questions about the role of static friction and torque in this scenario.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between applied force, static friction, and torque, questioning how the disk can rotate while its center of mass does not move initially. There are inquiries about the conditions under which friction can be less than the applied force and what factors determine the frictional force.

Discussion Status

The conversation is active with multiple interpretations being explored. Some participants suggest examining the equations of motion and torque to understand the frictional force better. Others raise questions about the conditions for terminal motion and the effects of energy loss in the system.

Contextual Notes

Participants are considering the implications of static versus kinetic friction and the conditions under which the disk rotates without slipping. There is an acknowledgment of external factors like air resistance and rolling resistance that may affect the motion of the disk.

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Homework Statement


A horizontal force is exerted on a uniform disk towards the center of mass resting on a horizontal table. The surface has friction. How does the disk begin to move ? Because when the force increases from zero, at first the friction is static friction which means the net force is still zero but the static friction can form a torque on the disk which will make it rotate. It is absurd that the center of the disk is at rest while the disk begins to rotate.


Homework Equations





The Attempt at a Solution


 
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Hi VictoriaWoo! Welcome to PF! :smile:
VictoriaWoo said:
How does the disk begin to move ? Because when the force increases from zero, at first the friction is static friction which means the net force is still zero but the static friction can form a torque on the disk which will make it rotate. It is absurd that the center of the disk is at rest while the disk begins to rotate.

The friction is less than the applied force …

so the torque is "forward", and the centre of mass moves forward …

the rolling constraint, v = rω , combined with the equations for force and torque, enable you to find the friction force :wink:
 
If the friction is smaller then the force applied to its center of mass there is a net force on the body, this causes body to accelerate in the direction of the net force a = F/m.
 
Why the friction can be smaller than the force? What determines the friction? And how does a disk rotating on a horizontal surface with friction come to terminal when it rotates without slipping and static force does not turn the kinetic energy into heat?
 
VictoriaWoo said:
Why the friction can be smaller than the force? What determines the friction?

the rolling constraint, v = rω , combined with the equations for force and torque, enable you to find the friction force …

write out the equations, and see :smile:
And how does a disk rotating on a horizontal surface with friction come to terminal when it rotates without slipping and static force does not turn the kinetic energy into heat?

air resistance, and energy lost through deformation of the disk at the instantaneous point of contact (rolling resistance)
 

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