Forces of rolling

Homework Statement

A constant horizontal force Fapp of magnitude 10N is applied to a wheel of mass 10 kg and radius 0.30m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its centre of mass has magnitude 0.60m/s2. In unit vector notation, what is the frictional force on the wheel?

The figure in the book shows a wheel on a horizontal surface with the arrow representing the applied force pointing horizontally to the right from the centre of the wheel.

The Attempt at a Solution

I arrived at an answer of F = (4.0N)i. The correct answer is negative. Having given the matter some thought, this is my reasoning. In order for the wheel to rotate when the force is applied, the point on the wheel in contact with the surface must be pushed to the left by the force of friction. That explains the negative sign.

However, let's assume instead that the wheel is moving under the influence of a torque applied to centre, not a horizontal force. Now I'm visualizing the bottom of the wheel pushing against the surface to the left. If the wheel does not slip, the frictional must be countering slipping by pushing to the right.

Is my thinking correct or do I have it back to front?

BvU
Homework Helper
Your thinking is correct. In the exercise the wheel is pulled and the friction makes it turn (no friction -> no turning).
In your 'instead' case, the wheel turns and the friction is what causes the forward acceleration (no firction -> no forward acceleration).

Your thinking is correct. In the exercise the wheel is pulled and the friction makes it turn (no friction -> no turning).
In your 'instead' case, the wheel turns and the friction is what causes the forward acceleration (no firction -> no forward acceleration).
Thank you for clearing that up. Now let's consider a wheel rolling to the right with no applied force. In this case the friction must be acting to the right as well, yes? So as to provide a torque to counter the movement?

PhanthomJay
Homework Helper
Gold Member
Thank you for clearing that up. Now let's consider a wheel rolling to the right with no applied force. In this case the friction must be acting to the right as well, yes? So as to provide a torque to counter the movement?
If the wheel is rolling to the right at constant speed, with no applied force acting on it (neglecting air drag and rolling resistance), what is the net force acting on it?

BvU
Homework Helper
Actually, no ! No such thing as 'torque to counter the movement' exists. Once the wheel is rotating, it will keep rotating at the same angular speed until there is something to change that. Compare ##F = ma## with ##\tau = I\;\alpha##. Zero ##\alpha## means zero friction needed to maintain angular speed.

If the wheel is rolling to the right at constant speed, with no applied force acting on it (neglecting air drag and rolling resistance), what is the net force acting on it?
Actually I meant in a realistic situation, ie. the wheel slows and eventually topples.

BvU
Homework Helper
What slows the wheel ?

And do you realize that 'constant speed' and 'the wheel slows' are contradictory ? Sorry, two different authors.

And: Do you realize that 'no applied force' and 'the wheel slows' are contradictory ?

If the wheel is rolling to the right at constant speed, with no applied force acting on it (neglecting air drag and rolling resistance), what is the net force acting on it?
The net force would be zero. So the friction which allows the wheel to move without slipping is not the one that causes it to slow down?

What slows the wheel ?

And do you realize that 'constant speed' and 'the wheel slows' are contradictory ?
True, but I should have clarified that I was not referring to constant speed in the third case. I meant, what happens if you roll it along the ground in real terms.

BvU