# Two balls same radius and mass rolling down a slope

• Nina87
In summary, the question asks which of two balls, one made of iron and one made of lead, with equal radius and mass, will roll down a slope faster. After discussing the relationship between kinetic energy and moment of inertia, it is determined that the ball with the smaller moment of inertia will roll faster. Therefore, assuming that the iron ball has a smaller moment of inertia than the lead ball, it will roll down the slope faster due to its higher angular velocity.
Nina87
two balls, one made of iron and one made of lead with same radius and mass. which one will roll down the slope faster?

i don't really know where to begin, since everything is the same, the only idea i had was to somehow relate Ek=(J.ω2)/2 => Ek= m.r2.(ω2/2) to the question since i imagine that for them to r1=r2, m1=m2 one must have thinner wall. but then i can't isolate 'v' from the equation to actually prove something.

Nina87 said:
two balls, one made of iron and one made of lead with same radius and mass. which one will roll down the slope faster?

i don't really know where to begin, since everything is the same, the only idea i had was to somehow relate Ek=(J.ω2)/2 => Ek= m.r2.(ω2/2) to the question since i imagine that for them to r1=r2, m1=m2 one must have thinner wall. but then i can't isolate 'v' from the equation to actually prove something.

Hi Nina87, Welcome to Physics Forums.

I think that you're thinking along the right lines. First determine which of two spheres with equal radii and mass but different moments of inertia will roll faster. You don't need any particular numbers to do this, just see how the acceleration or velocity depends upon the moment of inertia.

With that established, pick a method for making your lead ball of equal mass to the iron one. One way would be to hollow out a small sphere of appropriate mass from the center of the lead sphere. What would be the moment of inertia of the result? Larger or smaller than that of the solid iron sphere?

so as i understand with increasing radius increases moment of inertia.the moment of inertia of an object is a measure of how difficult it is to start it spinning. and as i imagine it,some parts of the iron ball are closer to the axis, therefore it has smaller moment of inertia (J=m.r2) compared to the lead ball(the task doesn't specify that one is solid and another is not).
i still don't know how velocity depends upon moment of inertia but my best guess is that since both balls are of equal mass they have equal potential energy. Ep= - Ek; Ek= (J.ω2)/2 so then it follows that their J & ω are different. assuming that the iron ball has smaller moment of inertia, it's ω must be bigger than the one of the lead ball.
v=r.ω (radii are equal; velocity of the iron ball is bigger).

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## 1. What is the relationship between the radius and mass of two balls rolling down a slope?

The radius and mass of two balls rolling down a slope have a direct relationship. This means that as the radius increases, the mass also increases, and vice versa. This relationship is due to the fact that the mass of a sphere is directly proportional to its volume, which is determined by its radius.

## 2. Does the angle of the slope affect the speed of the two balls?

Yes, the angle of the slope does affect the speed of the two balls. A steeper slope will result in a greater acceleration, causing the balls to roll faster. On the other hand, a gentler slope will result in a slower acceleration and a slower speed for the balls.

## 3. How does the surface of the slope affect the rolling of the two balls?

The surface of the slope can have a significant impact on the rolling of the two balls. A smoother surface will result in less friction, allowing the balls to roll faster and farther. A rougher surface will create more friction, causing the balls to roll slower and for a shorter distance.

## 4. Is there a difference in the rolling motion of the two balls if one has a hollow center?

Yes, there will be a difference in the rolling motion of the two balls if one has a hollow center. The ball with a hollow center will have a lower moment of inertia, meaning it will be easier to rotate and will roll faster compared to the solid ball with the same mass and radius.

## 5. How does the air resistance affect the rolling of the two balls?

Air resistance can have a significant impact on the rolling of the two balls. As the balls roll down the slope, they will encounter air resistance, which will slow them down. This means that the balls will not reach their full potential speed and will not roll as far as they would on a vacuumed surface.

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