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

[VictoriaWoo]

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

 

[tiny-tim]

Welcome to PF!

Hi VictoriaWoo! Welcome to PF!

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

 

[amiras]

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.

 

[VictoriaWoo]

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?

 

[tiny-tim]

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 ​

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)