Rolling object and friction

[kasse]

[SOLVED] Rolling object and friction

Homework Statement

I want to find an expression for the coefficient of friction when this object starts to skid when we pull it with a force F

http://www.badongo.com/pic/3639015

The Attempt at a Solution

F_f = (mju)*Mg

I found that I can put this into Newton's 2. law for rotation and solve for alpha = 0. But why can't I put it into Newton's 2. law for linear motion and solve for alpha = 0 (a = (alpha)*R)?

 

[Doc Al]

But why can't I put it into Newton's 2. law for linear motion and solve for alpha = 0 (a = (alpha)*R)?

You can certainly apply Newton's 2nd law for translational motion. But "a = (alpha)*R" only applies when it rolls without slipping, which is not the case here.

 

[Moetasim]

When dealing with a rolling object, we must consider both linear and rotational motion. The equation you have used, Ff = (mju)*Mg, represents the force of friction acting on the object when it is in a state of rolling without slipping. This means that the object is not skidding or sliding, but rather rolling smoothly. In this case, the net force on the object is equal to zero, and the object will continue to roll at a constant velocity.

However, when we apply a force F to the object, it may start to skid or slip, depending on the magnitude of the force and the coefficient of friction. In order to find the coefficient of friction when the object starts to skid, we must consider the rotational motion. This is because when the object starts to skid, the point of contact between the object and the ground becomes the point of rotation, and the object will start to rotate around this point.

To find the coefficient of friction in this case, we can use Newton's second law for rotation, which states that the net torque on an object is equal to the moment of inertia times the angular acceleration. We can set the torque due to the force F (τ = FR) equal to the torque due to friction (τ = FfR), and solve for the coefficient of friction (mju). This will give us the value of the coefficient of friction when the object starts to skid.

In summary, when dealing with a rolling object and friction, it is important to consider both linear and rotational motion. While we can use Newton's second law for linear motion to find the coefficient of friction in some cases, when the object starts to skid, we must use Newton's second law for rotation to accurately determine the coefficient of friction.