# Rolling Objects, Friction, and Newton's Second Law

• Starwing123
In summary, rotational dynamics problems involve finding the acceleration of a ring rolling down a hill with an angled surface. The equations used are for torque and force, and they give the correct answer when plugged in and solved. However, if the angle is 0, the equation for force does not make sense as it would imply that the ring is slowing down without rolling friction. This is because static friction is not a defined force and has a maximum value. Similarly, when pulling a yoyo vertically, it will not start to move horizontally, but it will detach from the ground and start to rotate. This is because the torque causes it to rise and rotate, rather than move horizontally. Newton's second law still applies in this scenario.
Starwing123

## Homework Statement

In rotational dynamics, a typical problem would be along the lines of a ring with mass m and radius r rolling down a hill with angle θ to the horizontal. Find the acceleration of the ring.

## Homework Equations

Ʃτ=I$\alpha$ = r x (friction)
ƩF = ma = mgsinθ - (friction)

## The Attempt at a Solution

These equations usually give the correct answer for the problem (plug in the numbers, isolate, solve for whatever the question asks). My question is that these equations don't seem to make sense if θ=0. That would imply that F = -(friction) and the ring is slowing down (if it was moving originally). However, that is not the case if there is no rolling friction. Why does this equation break down?

A similar dilemma I have is given a yoyo on the floor, if you pull vertically up on the string, the yoyo rolls in a certain direction. However, there is no net force horizontally, so how does it roll? If the answer is that the torque causes it, when why would Newton's second law even apply in the case of yoyos rolling down a string in midair?

Starwing123 said:

## Homework Statement

In rotational dynamics, a typical problem would be along the lines of a ring with mass m and radius r rolling down a hill with angle θ to the horizontal. Find the acceleration of the ring.

## Homework Equations

Ʃτ=I$\alpha$ = r x (friction)
ƩF = ma = mgsinθ - (friction)

## The Attempt at a Solution

These equations usually give the correct answer for the problem (plug in the numbers, isolate, solve for whatever the question asks). My question is that these equations don't seem to make sense if θ=0. That would imply that F = -(friction) and the ring is slowing down (if it was moving originally). However, that is not the case if there is no rolling friction. Why does this equation break down?

It does not break down. It simply means that the static friction is zero and the ring rolls with uniform velocity. You know that static friction is not a defined force, you only know its maximum possible value.

Starwing123 said:
A similar dilemma I have is given a yoyo on the floor, if you pull vertically up on the string, the yoyo rolls in a certain direction. However, there is no net force horizontally, so how does it roll? If the answer is that the torque causes it, when why would Newton's second law even apply in the case of yoyos rolling down a string in midair?

The yoyo will not start to move horizontally if you pull the string exactly vertical. But it will rise a bit, detached from ground and starting to rotate...

ehild

## 1. What is the relationship between rolling objects and friction?

The rolling motion of an object is affected by the force of friction acting on it. Friction can either help or hinder the rolling motion, depending on the surface the object is rolling on. For example, rough surfaces create more friction, slowing down the rolling object, while smooth surfaces create less friction, allowing the object to roll further.

## 2. How does Newton's Second Law apply to rolling objects?

Newton's Second Law states that an object's acceleration is directly proportional to the net force acting on it and inversely proportional to its mass. This law applies to rolling objects as well, as the force of friction acting on the object affects its acceleration. The heavier the object, the greater the force of friction needed to stop or slow down its rolling motion.

## 3. Can friction ever be eliminated in rolling objects?

No, friction can never be completely eliminated in rolling objects. Even on surfaces that seem smooth, there are microscopic imperfections that create friction. However, friction can be reduced by using materials that have low coefficients of friction, such as ball bearings, to facilitate smoother rolling motion.

## 4. How is the coefficient of friction determined for rolling objects?

The coefficient of friction for rolling objects is determined by dividing the force of friction by the normal force. The normal force is the force exerted by the surface on the object perpendicular to the surface. This value can be measured experimentally by measuring the force needed to keep the object rolling at a constant speed.

## 5. How does the surface affect the rolling motion of an object?

The surface an object is rolling on can greatly affect its rolling motion. Rough surfaces create more friction, making it more difficult for the object to roll, while smooth surfaces create less friction, allowing the object to roll further. Additionally, different surfaces may have different coefficients of friction, which can also affect the object's rolling motion.

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