Why does the wheel roll without sliding when accelerating?

[rainstom07]

In the figure http://i.imgur.com/LjFDg.gif, a wheel rolls horizontally without sliding while accelerating with linear acceleration \vec a_{com}. A static frictional force \vec f_s acts on the while at P, opposing its tendency to slide.

This is more of an coursework question.

When the textbook say "tendency to slide," what do they mean by that? Is it similar to driving up to 60 mph and then slamming on your brakes? If so, wouldn't the direction of the frictional force be in the opposite direction of the car?

Why is the static frictional force pointing in the direction of the acceleration of the center of mass, shouldn't it be the other way? If the figure is true,... then the wheel wants to slide backwards: sort of like moon walking?

 

[rcgldr]

The problem doesn't state the source of the acceleration. Apparently for this problem, it's due to an internal torque, such as an engine propelling a car.

 

[tiny-tim]

hi rainstom07!

… wouldn't the direction of the frictional force be in the opposite direction of the car?

Why is the static frictional force pointing in the direction of the acceleration of the center of mass, shouldn't it be the other way? If the figure is true,... then the wheel wants to slide backwards: sort of like moon walking?

for the direction of friction in rolling cases, consider what would happen if the surfaces became frictionless

the important piece of information is that the wheel is accelerating forwards

so the engine is accelerating it clockwise (as seen in the diagram)

suppose the road suddenly turned to ice …

the (linear) speed would stay the same, but the angular speed would increase …

so which way would the wheel slide? ​

 

[rainstom07]

so which way would the wheel slide?

Forward?

I suppose the wheels would just spin faster and faster, but it's linear velocity would not change.

I still don't understand why the force of friction is in the +x direction. Is it because the wheel is in a clockwise motion? If so, then --- in the figure http://i.imgur.com/uz2Rx.gif --- why is the force of friction pointed upwards towards the ramp? It doesn't seems like the direction of rotation is relevant to determining how the wheels will slide.

 

[tiny-tim]

so which way would the wheel slide? ​

I suppose the wheels would just spin faster and faster, but it's linear velocity would not change.

that's correct

and since the bottom of the wheel is always moving backward relative to the centre of the wheel, that means … ?

… in the figure http://i.imgur.com/uz2Rx.gif --- why is the force of friction pointed upwards towards the ramp? It doesn't seems like the direction of rotation is relevant to determining how the wheels will slide.

the direction of rotation isn't relevant

the direction of torque (about the centre of mass), and of linear force is relevant

in the original example, the torque is clockwise, and the linear force (on ice) is zero

in the new example, there is no torque (the weight is through the centre of mass), and the linear force is downward