# What is Rolling: Definition and 1000 Discussions

Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are in contact with each other without sliding.
Rolling where there is no sliding is referred to as pure rolling. By definition, there is no sliding when there is a frame of reference in which all points of contact on the rolling object have the same velocity as their counterparts on the surface on which the object rolls; in particular, for a frame of reference in which the rolling plane is at rest (see animation), the instantaneous velocity of all the points of contact (e.g., a generating line segment of a cylinder) of the rolling object is zero.
In practice, due to small deformations near the contact area, some sliding and energy dissipation occurs. Nevertheless, the resulting rolling resistance is much lower than sliding friction, and thus, rolling objects, typically require much less energy to be moved than sliding ones. As a result, such objects will more easily move, if they experience a force with a component along the surface, for instance gravity on a tilted surface, wind, pushing, pulling, or torque from an engine. Unlike cylindrical axially symmetric objects, the rolling motion of a cone is such that while rolling on a flat surface, its center of gravity performs a circular motion, rather than a linear motion. Rolling objects are not necessarily axially-symmetrical. Two well known non-axially-symmetrical rollers are the Reuleaux triangle and the Meissner bodies. The oloid and the sphericon are members of a special family of developable rollers that develop their entire surface when rolling down a flat plane. Objects with corners, such as dice, roll by successive rotations about the edge or corner which is in contact with the surface. The construction of a specific surface allows even a perfect square wheel to roll with its centroid at constant height above a reference plane.

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1. ### Why Is Deriving the Motion Formula for Hoops More Complex?

I've worked out how to derive the formulas for a solid cylinder and a solid sphere rolling down a hill. E.g., for a cylinder: Emech = KE + PE mgh = 1/2 mv^2 + 1/2 Iw^2 gh = 1/2 v^2 + 1/2 (1/2r^2) v^2/r^2 gh = 3/4 v^2 v^2 = 4/3 gh I then performed a derivative with respect to time and found a...
2. ### Rolling Motion (Stone Gets Stuck in a Tire Going Forward)

So I thought the stone would initially experience acceleration in the backward (leftward) direction then continually accelerate in the inward direction of the tire (i.e. upward then rightward then downward then leftward, etc.) as the tire moves forward. But the answer is immediately upward...
3. ### Motion of Sphere Rolling Down Rotating Cone

I am trying to understand the motion of the sphere in the image above, and I am a bit confused about the motion. How does the ball move down the cone? Will the rotation of the cone cause the ball to rotate with it, and which direction would the static friction be in? What does the path the ball...
4. ### Wooden sphere rolling on a double metal track

About points 1. and 2., I assumed that the point of the sphere moving with maximum velocity is ##Q## and that the velocity at that point is ##v_Q= 2v##. In fact, at the highest point of a rotating sphere, the velocity is given by the sum of the velocities of translation and rotation. Since, in a...
5. ### B Two points of contact in rolling

Suppose a sphere is rolling on horizontal surface. The point of contact is the instantaneous center of rotation. It's velocity momentarily is zero. So in a time dt it'll stay where it is. However during this time dt the point next to this contact point at its right side will move forward and...
6. ### Solve First Year Harmonic Motion Problem: Cylinder Rolling

Thank you guys for taking the time to read this - I'm decently struggling with first year and need some tips on how to properly conceptualize problems and learn what the right approach is on certain problems. Have a wonderful day, again thank you for checking this post out!
7. ### Kinetic Energy of a Cylinder Rolling Without Slipping

Given that there is a cylinder rolling without slipping down an incline, the method I was taught to represent the KE of the cylinder was: ##KE_{total} = KE_{translational} + KE_{rotational}## ##KE_{total} = \frac {1} {2} mv_{cm}^2 + \frac1 2 I \omega^2## Where "cm" is the center of mass, and...
8. ### I Rolling Motion direction of Velocity center of mass

Hi I have come across something confusing in rolling motion. If an object moves with a positive V_cm meaning to the right its angular velocity will be clockwise or negative. The formula is V_cm=wR but for a positive V_cm you get a negative w as it moves clockwise if V_cm is to the right...
9. ### The final velocity of a ball rolling while slipping.

Here is the problem statement along with the figure. Here, I take the right-ward and anti-clockwise directions to be positive. After the ball collides with the wall, its angular velocity remains the same and its velocity changes direction while remaining the same in magnitude. Using the...
10. ### Is Centrifugal Force the Key to Understanding Rolling Coin Dynamics?

I reasoned that at the coin's slowest velocity, the energy it has must just be enough for it to reach the highest potential configuration: when the point mass is directly above the centre of mass of the coin, and its GPE is ##mg(R+r)##. I used this to find the minimum velocity, but I can't think...
11. ### Moment of inertia problem involving a cylinder rolling down an incline

a=2/3*g*sin(25*(pi/180))=>a=2.8507 m/s^2 vf=vi+at=>vf=0+2.8507*1.50=>vf=4.2760 m/s So the translational motion of the cylinder is 4.2760 m/s. 4.2760=R*w w=134.04 rad/s PE=mgh=>PE=215*9.8*.108=>PE=227.56 J PE = KE at the end of the roll because of energy conservation. 227.56 =...
12. ### I Rolling ball, change of direction

Say I have a magic way to exert lateral forces on a free-rolling ball on a plane, with no slipping. Say I apply a force for a given period from the South, the ball starts rolling to the North and attains a constant speed. Then I suddenly apply the same force for the same period but from the...
13. ### Conductor rolling down an inclined plane in a vertical B-field

For part (c) of this problem, My working is However, the tricky part is to find theta. I tried to draw the situation so that I could find theta: It appears that theta = 90 degrees. However, this does not seem to be correct. Does anybody please know how to correctly find theta in terms of...
14. ### Coefficient of rolling resistance

Hi, What is the formula or methodology for finding the Crr? There are many of those tests done on the internet, but none state the procedure of calculation. I'm trying to find the correlation between tire pressure and distance and want to use Crr as one of the key factors influencing it. Maybe...
15. ### Describing Rolling Constraint for Rolling Disk With No Slipping

Let ##R=\sqrt{x^{2} + y^{2}}##. Then \begin{align}v_{tangential}&=\frac{dR}{dt} \nonumber\\ &=\frac{dR}{dx}\frac{dy}{dt} + \frac{dR}{dy}\frac{dy}{dt} \nonumber\\ &=\frac{x}{R}\frac{dx}{dt} + \frac{y}{R}\frac{dy}{dt} \nonumber\\ &= cos\phi \frac{dx}{dt} + sin\phi \frac{dy}{dt}.\nonumber...
16. ### Rolling mill force calculations

Hi, I'm building a rolling mill for flattening out bits of steel and I'm trying to make sure it's not going to break. I know that with a 1500w motor geared down to 60rpm (2pi rad/s) i end up with 239Nm of torque. 239Nm working at a radius of 0.0375m gives 6369N of force generated at the edge...
17. ### B Why is static friction necessary for pure rolling?

Suppose a cylinder is launched on a horizontal frictional surface such that it has initial translational velocity v and zero angular velocity .the kinetic friction would be applied between the contact points of the cylinder and the surface, opposite to the direction of the translational motion...
18. ### B Rolling of non-deforming sphere on a non-deforming rough surface?

According to my current understanding rolling friction rolling friction is the static friction (parallel to the surface on which the object is moving) applied by the frictional surface (rough surface) on the contact point or contact area of the object whose v≠Rw(v is translational velocity and...
19. ### Question regarding Rolling with and without Slipping and Sliding

1)When a wheel is stuck in mud it rolls with slipping ,this means that at the point of contact it has a net velocity As we can see from the image Kinetic Friction acts in the direction opposite to the resultant velocity ,this effectively reduces the tangential velocity at the surface and tries...
20. ### B Trouble understanding what rolling friction is

In pure rolling the of the sphere contact points of the sphere are at zero velocity,how is friction opposite to the motion of sphere being applied to these points?how the frictional force f is bieng applied to the sphere?
21. ### B Friction on pure rolling non deforming sphere?

How will the friction work on a sphere which is purely rolling on a horizontal surface such that both the sphere and surface does not deform. The sphere at any time t will only have one point of contact, which would continuously changing as the sphere rolls. Will The friction be applied to the...
22. ### I Friction in rolling without slipping

Consider an object, say a ball, rolling at a constant speed without slipping to the right on a horizontal surface. Let's consider the ideal case, so no deformation of ball or surface. For rolling without slipping to occur, there has to be friction (static friction as the point on the ball that...
23. ### Acceleration of system related to rolling motion and pulley

There is no friction mentioned by the question so I assume the plane is frictionless but can the sphere roll without slipping if there is no friction? This is my attempt: Equation of translation motion of object A (assuming A moves upwards): TA - WA sin θ = mA . aCOM (A) TA = mA . aCOM (A) + WA...
24. ### Direction of friction on rolling object

A force is given to the center of the object so the object rolls to the right without slipping. I understand that to provide clockwise rotation the static force should be directed to the left. But if the force F is located at the very top of the object, the static friction is directed to the...
25. ### B Rolling Motion Test: Take the Challenge and Justify Your Answers

I am posting this to generate a parallel discussion to this ongoing thread. It seems that some participants in that thread have doubts and confusion about rolling motion that might be better addressed separately from the homework problem in question. It is a simple test of one's understanding...
26. ### I Friction of a rolling cylinder on an incline

Hello everyone! I'm watching this Walter Lewin lecture and am at 5:58 part of the video I'm wondering how there's a frictional torque applied to the cylinder, my reasoning is that the object has forward velocity, and on a perfect cylinder, the slope of the incline touches the cylinder at a...
27. ### How can we model a rolling truck on an incline using rotational motion analysis?

This is a problem that was posted here in 2003 and is now closed for replies. This question can be found at https://www.physicsforums.com/threads/friction-problem.662/ The answer in that old post didn't seem clear to me probably because it was highly summarized. There was no mention of static...

29. ### Constraints on a hoop rolling on a cylinder

My question is about the contraint we need to use to solve this problem. The answer to the question use the following constraint: $$(r+R)\theta = r\phi$$ Where $\theta$ is angle from the radius of the fixed cylinder to, say, the vertical axis. And $\phi$ is the angle that the rolling cylinder...
30. ### B Rolling without slipping in non-sloping surface

Suppose we leave an object on a non-sloping surface that rolls and moves forward without slipping. Does this object continue to move indefinitely?
31. ### Ball rolling down a slope problem: Find an expression for time taken

Question: Galileo released a metal ball from rest so that it could roll down a smooth inclined plane. The time t taken to roll a distance s was measured. He repeated the experiment, each time recording the time taken to travel a different fraction of the distance s. Write an expression for the...
32. ### Potential difference of a ring rolling in magnetic field

I don't understand why there is potential difference between point A and O. Is there any change in magnetic flux experienced by the ring? I think the magnetic field passing through the ring's cross sectional area is constant Thanks
33. ### A sphere rolling without slipping down a hemisphere

a) From impulse-momentum theorem I have: ##J=mv## so ##v=\frac{J}{m}## and since the ball doesn't slip ##v=\Omega b## so ##\Omega=\frac{J}{mb}## and ##\dot{\theta}=\frac{v}{a+b}=\frac{\Omega b}{a+b}##. b) I considered the angular impulse: ##-J(a+b)=I_0 \Omega_0 \Rightarrow...
34. ### A rolling ball, find distance traveled

I figured the best way to do this is to focus on the second half of time. We can use the information there to find acceleration and that should make it fairly simple to find distance traveled in the first 5 seconds. Average speed in 5s-10s I found to be 40m/s. My problem is that to find the...
35. ### Torque exerted on rolling cylinder

Hello, i have tried to calculate the acceleration (COM) of the cylinder (even though in the question they asked about the angular acceleration) and the answer is: 𝑎(𝑐𝑜𝑚)=𝐹(𝑟/𝑅−𝑐𝑜𝑠(𝑡ℎ𝑒𝑡𝑎))/(𝐼/𝑅2+𝑀) and my answer is with minus (I/R^2 - M) . in their solution they wrote in the torque equation-->...
36. ### Ball rolling down a slope ending with a loop

Hello everyone! I tried to solve this problem in a non-inertial system. Probably I should use the principle of conservation of mechanical energy in the following form $$mgH = \frac{3mgR}{2} + \frac{mV^2}{2}.$$ So the only thing to do is to compute $V^2$. I tried to find this value using the...
37. ### I Coefficient of rolling friction for a lab cart

I was looking for a way to calculate the friction arising from the axle and wheel of a standard lab cart. I came across this research paper: https://www.usna.edu/Users/physics/mungan/_files/documents/Publications/PhysEd4.pdf That derived the following equation for the coefficient of rolling...
38. ### Free body diagram for an inverted pendulum in the rolling sphere

So, to obtain the motion equations I initially plotted the free-body diagram (see picture). Then I’ve tried to get equations, but I’m not sure, do I have done it rightl. I will be gratefull if someone could help me.
39. J

### I Gravitational Illusions -- Two balls rolling down differently-shaped ramps

Without this test,using only math, would you prove that left ball will comes first?
40. ### A Cylinder Rolling in a V-Groove

I am confused because according to my solution the disk is already rotating at constant angular velocity. I have written the translational equilibrium on the horizontal and vertical component: ##N_1## and ##f_2## will have a positive horizontal contribution, while ##N_2## and ##f_1## will have a...
41. ### Speeds of the rolling ball at different points in this roller coaster track

For this question i tried to reason with my self that C was the fastest and A was the second fastest. B would be the third fastest and D would be the least fastest since the ball has to go up. I looked up the answer and it says that C is the fastest , B and D are equal, and A is the slowest. How...
42. ### Rolling without slipping down an inclined plane

The acceleration and velocity of a body rolling down without slipping on a frictionless inclined plane are given by $$a=\dfrac{mg\sin \theta }{m+\dfrac{I}{r^{2}}}=\dfrac{g\sin \theta }{1+\dfrac{K^{2}}{r^{2}}} \cdots(1)$$ ...
43. ### I Rolling balls with different rotational inertia

I am stuck on problem presented about putting golf balls. A stationary golf ball (mass=45g, dia=42mm, solid & homogeneous) is struck by a horizontal force (putter) and ignoring sliding immediately starts rolling on a level putting green. The ball eventually stops due to rolling resistance...
44. ### Expected value of median of rolling three fair dice

Hi, I was reading this problem and I found a solution on Math Stackexchange which I don't quite understand. Question: Calculate the expected value of the median of rolling a die three times. Attempt: I read the following answer on math stack exchange here "As already noted in a comment, the...
45. ### Motion of Rolling Cylinder in Fixed Cylinder: Confusing Constraint Condition

The problem is a classical one, basically to find the equations of motion of cylinder of radius a inside a fixed cylinder of radius b, the cylinder that rolls rotate about its own axis in such way that it does not skid/slip. Now, the thing that is making myself confused is the constraint...
46. ### Automotive Speed of a car rolling down a hill

This looks like a physics question but it's not; it's an automotive question. Suppose you had a car at the top of a gently sloped hill, a 5% grade. You start it and put it in neutral or drive and it starts to roll down. You never place your foot on the brake or the accelerator and suppose the...
47. ### Derive the period of a Ball rolling in a Bowl

The following attempt gives the wrong answer, and I would like to know where it goes wrong. Let ##\theta## be the angle of the ball with the vertical passing through the centre of the bowl, and ##\phi## be the angle the ball rolls through. Let ##m## be the mass of the ball, ##r## be the radius...
48. ### MHB Probability of Rolling Sum > 3 with Two Dice

Two fair dice are rolled. What is the probability of rolling a sum that exceeds 3?

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50. ### Engineering Rigid wheel rolling without slipping -- Trying to find angular acceleration

So I tried the problem and it’s different from the solution. I’m confused on why my attempt didn’t work, is it because the wheel is undergoing general planar motion? I tried to just apply Newton’s 2nd law to find the acceleration of the centre and then use that to find angular acceleration. The...