Friction acting on rolling wheel

In summary: Assuming the wheel doesn't slip, this means that the friction force at the contact point with the ground must be large enough to provide this torque. So set up an equation for the torques and solve for the minimum friction force required to lift the wheel.In summary, a constant horizontal force of 12 N is applied to a wheel of mass 8 kg and radius 0.70 m, resulting in a smooth roll with an acceleration of 0.75 m/s2. The frictional force on the wheel can be calculated using Newton's 2nd law applied to both rotation and translation, and is found to be -6 N. The rotational inertia of the wheel about its center of mass is 3.92 kg
  • #1
mbrmbrg
496
2

Homework Statement



In Figure 11-30(see attatched), a constant horizontal force F_app of magnitude 12 N is applied to a wheel of mass 8 kg and radius 0.70 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.75 m/s2.

(a) In unit-vector notation, what is the frictional force on the wheel?
[? Ni]
(b) What is the rotational inertia of the wheel about the rotation axis through its center of mass?
[3.92 kg*m^2 ]


Homework Equations



[tex]\tau=r\times F[/tex]

[tex]\tau=I\alpha[/tex]

[tex]I_{hoop}=mr^2[/tex]

[tex]\alpha=\frac{a_{com}}{r}[/tex]


The Attempt at a Solution



I took the axis of rotation to be perpindicular to the wheel's center of mass.

There are four forces acting on the wheel: mg, normal, applied force, and friction. Of those four forces, only friction does not pass through the axis of rotation, so friction alone (symbol is lowercase f) contributes to torque.

[tex]\tau=r\times f=I\alpha[/tex]
[tex]fr=(mr^2)(\frac{a_{com}}{r})[/tex]
[tex]f=ma_{com}(\frac{r^2}{r^2})[/tex]
[tex]f=(8kg)(.75m/s^2)=6N[/tex]
BZZZZZ. I lose.

Though on the bright side, my solution for the rotational inertia earned me a pretty green check mark...
 

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  • #2
mbrmbrg said:
There are four forces acting on the wheel: mg, normal, applied force, and friction. Of those four forces, only friction does not pass through the axis of rotation, so friction alone (symbol is lowercase f) contributes to torque.
All good.

Don't assume that the wheel can be modeled as a thin ring of mass. Instead, apply Newton's 2nd law twice: Once for rotation; once for translation (what's the net force on the wheel?). Combine those two equations to solve for f and I.
 
  • #3
Doc Al said:
Don't assume that the wheel can be modeled as a thin ring of mass.
But doing so gave me the correct rotational inertia...
Whoa, cool! solving for friction using translation then using that still gives me the right inertia! So neat when the physics works!
Instead, apply Newton's 2nd law twice: Once for rotation; once for translation (what's the net force on the wheel?). Combine those two equations to solve for f and I.
Using only translation, I solved for friction, and got the answer WebAssign wanted: -6N. But that gives friction pointing away from the direction of the overall motion of the wheel; it had taken me so long to comprehend that friction points in the same direction in which the body rolls!

Thanks!
 
  • #4
mbrmbrg said:
But that gives friction pointing away from the direction of the overall motion of the wheel; it had taken me so long to comprehend that friction points in the same direction in which the body rolls!
I hope you now realize that the friction force does not point in the same direction as the applied force. The wheel accelerates to the right, but friction acts to the left.
 
  • #5
Interesting. What if there was a blockade of some height (less than the radius of the wheel) was on its way? On that case how should one calculate the minimum force so as to just lift the wheel off the ground ? Any idea ?
 
  • #6
Slepton said:
Interesting. What if there was a blockade of some height (less than the radius of the wheel) was on its way? On that case how should one calculate the minimum force so as to just lift the wheel off the ground ? Any idea ?
Consider torques about the edge of the step it must get over.
 
  • #7
Hi Doc Al, could you explain a bit more ? Thanks
 
  • #8
Consider the forces acting on the wheel. For the wheel to get over the block or step, you must exert enough upward torque to balance out the downward torque due to gravity.
 

1. What is friction acting on a rolling wheel?

Friction acting on a rolling wheel refers to the resistance force that occurs between the wheel and the surface it is rolling on. It is caused by the microscopic imperfections on both surfaces that come into contact with each other.

2. How does friction affect the movement of a rolling wheel?

Friction can slow down the movement of a rolling wheel, as it acts in the opposite direction of the wheel's motion. It can also cause the wheel to roll in a different direction than intended if the surface is not completely flat.

3. What factors can affect the amount of friction on a rolling wheel?

The amount of friction on a rolling wheel can be affected by the weight of the wheel, the texture and condition of the surface it is rolling on, and the speed at which the wheel is rolling.

4. How can friction on a rolling wheel be reduced?

Friction on a rolling wheel can be reduced by using lubricants, such as oil or grease, to create a smoother surface between the wheel and the surface it is rolling on. Additionally, using wheels with a larger diameter or adding ball bearings can also help reduce friction.

5. Can friction on a rolling wheel ever be completely eliminated?

No, friction on a rolling wheel can never be completely eliminated. However, it can be reduced to a certain extent by using various methods such as lubrication or using smoother surfaces. In a perfect scenario, with no microscopic imperfections, there would be no friction between the wheel and the surface.

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