What is the direction of friction when a spool of wire is rolling on the ground?

In summary, the direction of friction acting on a spool of wire depends on the relative radius of the wire and the spool, and the ratio of their masses. If the radius of the wire is smaller than half the radius of the spool, the friction acts in the opposite direction of the tension force. If the radius of the wire is equal to half the radius of the spool, there is no friction. If the radius of the wire is greater than half the radius of the spool, the friction acts in the same direction as the tension force. This can be determined mathematically by considering the torque and force equations and the relationship between angular acceleration and linear acceleration.
  • #1
pradeepk
19
0
In class the other day, my professor began talking about spools of wire on the rolling on the ground and when drawing their free body diagrams, he sometimes made the friction acting in the same direction as the motion of the spool. This really confused me, and I was just wondering if anyone could tell me, when friction acts in the same direction as the motion?
Thanks a lot.
 
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  • #2
It's actually depends to:
- Inertia of the spool (1/2 MR or the others)
- The location and direction of the tension force to the center mass of the spool
by some mathematics algebra from torque equation, force equation, and the relation of the angular acceleration and the acceleration you will get value of critical radius of spool that the direction of the friction depends on the radius whatever it's more than or less than the critical radius.
However, I'm sorry It's hard to me to write all of the step in here. :redface:
 
  • #3
The only cases where rolling friction acts in the direction of motion is when there is deceleration due to an external force, such a gravity on a spool if it's rolling uphill.
 
  • #4
welcome to pf!

hi pradeepk! welcome to pf! :wink:

suppose the wire is being pulled to the right …

if the wire comes out under the spool, then the spool must move to the left, so the direction of friction has to be to the left! :smile:

if the wire comes out over the spool, then the spool must move to the right, so that doesn't help us much :redface:

so consider whether the torque from the wire makes the bottom of the spool want to move slower or faster than it actually is moving :wink:

(btw, the direction of friction on the non-driving wheels of a car always opposes the acceleration of the car)
 
  • #5


tiny-tim said:
hi pradeepk! welcome to pf! :wink:

suppose the wire is being pulled to the right …

if the wire comes out under the spool, then the spool must move to the left, so the direction of friction has to be to the left! :smile:

if the wire comes out over the spool, then the spool must move to the right, so that doesn't help us much :redface:

so consider whether the torque from the wire makes the bottom of the spool want to move slower or faster than it actually is moving :wink:

(btw, the direction of friction on the non-driving wheels of a car always opposes the acceleration of the car)


Ok I think I understand now. So in the first example, the force you are pulling with is to the right, however the spool moves to the left, so there must be some force causing it to go in that direction, and that force is friction? In the second example, it moves in the direction of the applied force, so it is just normal circumstances. Is that correct?
 
  • #6
If the wire is being unwound from the top, the direction of the force depends on the relative radius of the wire on the spool and also the ratio of mass of wire to mass of spool. If the radius is zero, it's the same as the spool being pulled from the center and the friction opposes tension. If the radius is large enough, then the friction is in the same direction as the tension.

For this mathematical example, assume the wire is massless, that the spool has the same angular inertia as a solid uniform cylinder, that the spool is rolling to the right, and that positive friction force means to the right.

R = radius of spool
r = radius of wire
t = tension
f = friction force (positive means same direction as tension)
m = mass
a = linear acceleration
α = angular acceleration
τ = torque
I = angular inertia = 1/2 m R2
c = r/R
a = -α R (rolling to right is clockwise)
α = -a / R

a = (f + t) / m
τ = f R - c R t = α I
f R - c R t = α (1/2 m R2)
f R - c R t = -a (1/2 m R)
(2f - 2ct) / m = -a = -(f+t) / m
3f = (2c -1) t
f = (2c - 1) / 3

In this case, if r/R is < 1/2, friction force is to the left (negative), if r/R = 1/2, friction force is zero, and if r/R > 1/2, then friction force is to the right (positive).
 
Last edited:

1. What is friction of a rolling object?

Friction of a rolling object is the resistance that occurs when an object rolls over a surface, resulting in a force that opposes the motion of the object.

2. How does the weight of an object affect its friction?

The weight of an object does not directly affect its friction. However, the weight of the object can affect the amount of normal force acting on the surface, which in turn can affect the friction force.

3. What factors can affect the friction of a rolling object?

The factors that can affect the friction of a rolling object include the weight and shape of the object, the type of surface it is rolling on, and the speed at which it is rolling.

4. What is the difference between static and kinetic friction of a rolling object?

Static friction occurs when an object is at rest and is about to start moving, while kinetic friction occurs when an object is already in motion. The force of static friction is typically greater than the force of kinetic friction.

5. How can friction of a rolling object be reduced?

The friction of a rolling object can be reduced by using a smoother surface, lubricating the surface, or reducing the weight of the object. Additionally, reducing the speed at which the object is rolling can also decrease friction.

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