What is Rolling motion: Definition and 99 Discussions

Rolling cone motion is the rolling motion generated by a cone rolling over another cone. In rolling cone motion, at least one of the cones is convex, while the other cone may be either convex, or concave, or a flat surface (a flat surface can be regarded as a special case of a cone whose apex angle equals



π


{\displaystyle \pi }
). The distinguishing characteristic of a rolling cone, in relation to other axially symmetrical rollers (cylinder, sphere, round disk), is that while rolling on a flat surface, the cone's center of gravity performs a circular motion rather than a linear one. Another unique characteristic is that one of its points (its apex) is at rest throughout the entire motion.

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  1. Q

    Rigorous proof about the nature of rolling motion

    In Resnick/Halliday, they describe how rolling can be described as the sum of a rotational force centered at the center of mass (for a wheel, say) and translational motion. The next part involves them saying that the motion can also be described as a completely rotational motion centered at the...
  2. Z

    Is Mechanical Energy Conserved in Rolling Motion without Slipping?

    Homework Statement The Attempt at a Solution In rolling without slipping, the friction does some work of torque about the axis of rotation. So mechanical energy is not conserved. A) - r),t) B) and C) - r),t) D) - One example I can think for the instant centre of rotation is...
  3. P

    Rolling Motion on Rough Surfaces

    Friction is necessary to make motion rolling but if the body is already in rolling motion on rough surface without slipping then, is friction necessary to continue the rolling motion ?
  4. F

    What is the relationship between constant speed rolling motion and friction?

    hi ,this is my first post (and its not HW) i currently study dynamics of rigid bodies using (Hibbeler) and there's one thing about this type of motion (rolling) that just seems to elude me for any planar motion we have 3 equations \Sigma F_{{x}}={\it ma}_{{g_{{x}}}} \Sigma F_{{y}}={\it...
  5. F

    How Does Rolling Affect Kinetic Energy Distribution?

    Homework Statement An 8 cm, 400 g sphere is released from rest at the top of a 2.1 m long, 25 degrees incline. It rolls, without slipping, to the bottom. a. What is the sphere's angular velocity at the bottom of the incline? b. What fraction of its kinetic energy is rotational? Homework...
  6. C

    What Are the Correct Terms for Rolling Wheels vs. Rolling Balls?

    Greetings, I have a peculiar terminological issue. In a research paper I am writing, I need to distinguish between rolling wheels and rolling balls. The relevant difference for my purposes is that a wheel rotates around a single axis whereas a ball rotates around a single point. It's...
  7. M

    Rolling motion of a cylinder down an incline

    Homework Statement Assuming smooth rolling with no resistance, it can be shown that the acceleration of a solid cylinder down an incline is equal to: a = 2/3 g sin(theta) The goal of my lab is to test the validity of the above equation Homework Equations The Attempt at a...
  8. B

    Rolling motion in a special ramp

    Homework Statement Assuming the sphere roles down without sliding prove that the acceleration of it's center of mass is: a= \frac{g\cdot \sin(\theta)}{1+\frac{2}{5}\cdot \frac{1}{1-\frac{1}{4}\cdot \xi^2}} Where \ \xi=\frac{L}{R} Note that the moment of inertia of the sphere is...
  9. S

    Force of Friction in rolling motion without knowing r

    Homework Statement A hollow spherical shell with mass 1.50 kg rolls without slipping down a slope that makes an angle of 39.0^\circ with the horizontal. a) Find the magnitude of the acceleration a_cm of the center of mass of the spherical shell. b) Find the magnitude of the frictional...
  10. K

    Calculating Speed of a Point on a Rolling Wheel

    Homework Statement A 60cm diameter wheel is rolling along at 20m/s. What is the speed of a point at the front edge of the wheel? Diameter - .6m Velocity - 20m/s Answer - 28m/s Homework Equations v = r(omega) Pythagorean theorem The Attempt at a Solution I tried to get...
  11. S

    Kinetic Energy in Rolling Motion

    Homework Statement Upon application of the 10-N force F to the cord in Figure P5.3, the cylinder begins to roll to the right. After C has moved 5 m, how much work has been done by F? do not have picture so let me decribe the picture: 1) cylinder with radius .5m is on the ground 2) the cord...
  12. N

    Rolling motion of an unbalanced disk

    Homework Statement The mass center G of a 5kg wheel of radius R = 300 mm is located at a distance r = 100 mm from its geometric center C. The centroidal radius of gyration is k = 150 mm. As the wheel rolls without sliding, its angular velocity varies and it is observed that it is = 8 rad/s in...
  13. E

    Minimum Coefficient of Friction for Non-Rolling Disk on Platform

    Homework Statement Question A disk is initially stationary on a platform. Force P is exerted on the platform. Mass of Disk is MD and Mass of Platform is MP. Determine the minimum coefficient of friction in order for the ball to not roll. What is the acceleration of the ball as seen from...
  14. J

    What Happens When a Slipping Sphere Begins to Roll Without Slipping?

    Homework Statement A uniform density sphere is released such that it has an angular speed of 10 rev/sec and no initial linear velocity. The angular velocity vector is perfectly perpendicular to the linear momentum vector. Initially the ball slips as it moves along the surface, but after...
  15. mr_sparxx

    Rolling motion on inclined plane: centre of mass acceleration, friction, torque

    Hi, When a circular section object (cylinder, sphere of radius r) rolls down an inclined plane (at angle theta) it experiences both linear and angular acceleration due to gravity. I have read multiple times that: mg sin(theta) - friction = m a where friction = Torque/r From there on...
  16. G

    Rolling Motion of a motorcycle

    Homework Statement Assume that there is no slipping of the surfaces in contact during the rolling motion. A motorcycle accelerates uniformly from rest and reaches a linear speed of 22.0 m/s in a time of 9s. The radius of each tire is 0.280 meters. What is the magnitude of the angular...
  17. M

    Rolling motion of a rigid body problem

    1. A solid sphere has a radius of 0.200 m and a mass of 150 kg. How much work is required to get the sphere rolling with an angular speed of 50.0 rad/s on a horizontal surface? Assume the sphere starts from rest and rolls without slipping 2. The attempt at a solution I found V first. V= rw =...
  18. J

    Does Increasing Torque Affect Kinetic Friction When a Wheel Slips?

    This isn't actually a homework question, but the style of it fits best in this forum. Diagram http://img355.imageshack.us/img355/9836/text5029jb0.png \tau - torque of wheel R - radius of wheel f_k - force due to kinetic friction Question Is the translational acceleration of the...
  19. B

    How Does Hitting a Cue Ball Above the Equator Affect Its Motion?

    Homework Statement A cue ball is hit 4.5 cm above the horizontal surface uk = 0.35 it is on. The ball is 6 cm in diameter and has a mass of 250 g. It is hit by a cue stick with an average force of 6000 N during a contact time of 20 usec. (a) What is the ball’s speed after it is hit...
  20. I

    Solving for Acceleration and Friction in Rolling Motion

    Here's the question: A solid sphere of mass M is being pushed by a plank of mass m along the top of the rim. Assuming pure rolling at all points of contact, find: (i) the accelerations of the centre of mass sphere and the plank w.r.t. ground. (ii) frictional forces operating at both the...
  21. I

    Is rolling resistance related to relative motion at the point of contact?

    When there is purely rolling motion in an inclined plane, it is mentioned that work done by the frictional force is zero! Why should it be zero as there is definitely a force as well as displacement in opposite direction of force? Is this true or for rolling motion there is some other...
  22. Z

    How Does Friction Affect the Rolling Motion of a Sphere?

    A perfect uniform sphere is thrown horizontally on to the floor. It slides on the floor then it begins rollings soon after. Draw a complete FBD and diagram for the motion before and after the rolling. ->My problem is does the kinetic friction act in the same direction as the balls motion or...
  23. B

    When does the ball start rolling without slipping?

    3. A solid rubber ball is thrown so that it has an initial horizontal velocity of 12 m/s on a flat horizontal concrete surface, but is not initially rotating. Eventually friction will induce the ball to roll without slipping. Assuming you can neglect rolling friction, a) determine the amount of...
  24. B

    Finding b for a Ball with Non-Uniform Density on a Circular Loop

    [/B]Homework Statement Hello: Can someone help with the following? A ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.48m. The initial height of the ball is h = 0.36m. At the loop bottom, the magnitude of the normal force on the ball...
  25. V

    Rolling Motion w/Static Friction

    Hey guys, I need help understanding why it is static friction that is involved in pure rolling motion? From what I remember in translational motion, when the maximum static friction force is overcome, then the given object/particle/body will start accelerating. Otherwise, the...
  26. A

    Rolling Motion without slipping Problem

    Homework Statement A small rubber wheel is used to drive a large pottery wheel, and they are mounted so that their circular edges touch. The small wheel has a radius of 2.0cm and accelerates at a rate of , and it is in contact with pottery wheel (radius 25.0 cm)without slipping. Calculate (a)...
  27. X

    Rolling motion including torque and acceleration

    Homework Statement A constant horizontal force \vec{F} is applied to a lawn roller in the form of a uniform solid cylinder of radius R and mass M. If the roller rolls without slipping on the horizontal surface, show that (a) the acceleration of the center of mass is \frac{2\vec{F}}{3M} and (b)...
  28. B

    Rolling Motion, a Contradiction

    For a wheel in pure roll, or smooth rolling motion, with constant angular velocity, \omega, the velocity of the point on the top of the wheel is 2v_{com}, and the velocity of the point at the bottom of the wheel is 0. (all relative to the ground) However, since centripetal acceleration is...
  29. N

    Kinetic Energy and Rolling motion

    A 500g, 8.0-cm-diameter can rolls across the floor at 1.0 m/s. What's the can's kinetic energy. I solved this using: K = \frac{1}{2}*I*(\frac{v}{r})^{2} and for some reason I get 1/3 the answer. So I multiplied it by 3 at the end. Is there something wrong with the formula I'm using...
  30. C

    Kinetic Energy of Rolling Motion

    Homework Statement A 12g CD with a radius of 7.0 cm rotates with an angular speed of 35 rad/s. What is its kinetic energy? Homework Equations The Attempt at a Solution I used K=(1/2)mv^2(1+I/mr^2) v=\omegar=(35rad/s)(0.07m)=2.45m/s K=(1/2)(0.012kg)(2.45m/s)^2(1)=0.36 And...
  31. R

    Kinematics of ball rolling motion

    Hi everyone, I'm kinda new and I'm trying to understand some kinematic principles which I can't really figure out... Without using intuition, what is the proof behind in explaining that the velocity of a rolling ball down a straight ramp increases and the velocity decreases when the...
  32. K

    How Does Friction Affect Energy Conservation in Rolling Motion?

    Hi, I got a doubt while studying rotational mechanics. It is said in my book that when a sphere is purely rolling on a surface, total mechanical energy is conserved even though friction is acting. Isnt friction an external force? How can energy be conserved then?? Another doubt I got is...
  33. D

    Sliding to Rolling motion problem.

    Homework Statement A bowling ball is released without spin. How far does it travel before its motion is pure, rolling motion? No data is given, it asks for an order of magnitude estimate. Homework Equations k = mv^2/2 k = Iw^2/2 + mR^2w^2/2 I = 2MR^2/5 torque = Ialpha torque = fk(R)...
  34. E

    Max Mass for Cylinder to Roll Without Slipping | Cylinder and Mass System

    Homework Statement The axle of a uniform solid cylinder of mass m1=7.1 Kg is attached to a string that runs over a massless, frictionless pulley. The other end of the string is attached to a mass m2. The coefficient of static friction between the cylinder and the table is U=0.202. What is the...
  35. H

    Rolling Motion Down an Incline

    The five masses below all have the same radius and a cylindrically symmetric mass distribution. They start to roll down an inclined plane, starting from rest, at the same time and from the same height. Give their order of arrival at the bottom. Icm=684 g*cm2, M = 47g Icm=373 g*cm2, M =...
  36. N

    Finding Frequency for Rolling Motion of Sphere in Spherical Bowl

    This problem has been driving me crazy. There is spherical ball of mass M and radius R. It is in a sphererical bowl with radius 10R. What is its frequency if pure rolling motion is assumed? I figured it out if there is no friction so it slips. Sum of Torque = I ddz/ddt = Mg10RsinZ I =...
  37. A

    How Does Applying an Impulse at a Distance Affect an Object's Motion in Space?

    I want to make a simple game, where you have a spaceship with thrusters on the left and right. Firing one at a time both spins and propels the ship. The problem is that, in physics 1000, we always assumed our rolling motion was on a surface, allowing us to relate the linear speed to the...
  38. L

    Rolling motion of a rigid body

    A ring of mass 2.4kg, inner radius 6c.0cm, and outer radius 8.0cm is rolling (without slipping) up an inclined plane that makes an angle of theta=36.9 with the horizontal. At the moment the ring is x=2.0 m up the plane its speed is 2.8 m/s. the ring continues up the plane for some additonal...
  39. K

    Solving Rolling Motion of Embedded Cylinder on Ramp

    Hi. I have a problem about rolling motion. Suppose that I have a large hollow cylinder. A smaller solid cylinder is embedded inside the larger hollow cylinder. http://www.geocities.com/andre_pradhana/cylinderkendro2.JPG When I positioned the cylinder on a flat ramp like the picture below...
  40. S

    Rolling Motion (Kinetic Energy)

    I have a question regarding the Rolling Motion equation. (1/2)Mv^2 + (1/2)I\omega^2 + Mgy (Where M=mass, v=velocity, I=moment of inertia,ω=angular velocity, g=force due to gravity and y = vertical distance) The problem I'm having involves the direction of the acceleration due to gravity...
  41. A

    Rolling motion linear and translation equation

    Hello well i have a very basic doubt well when we have a rolling motion and surface is rough then what i used to do was write linear and translation equation and find f (Frictional force) Now is this frictional force same as static friction and can we write is as kmg where k is coeffecient...
  42. K

    Rolling motion of plank and cylinders

    This will be a long thread... hope you'll take the time to read, cause I really need help. A plank with a mass M = 6.00 kg rides on top of two identical solid cylindrical rollers that have R = 5.00 cm and m = 2.00 kg. The plank is pulled by a constant horizontal force F of magnitude 6.00 N...
  43. A

    Rolling Motion of a Rigid Object

    I have no clue where to start on this problem. I appreciate any help. Thanks. A uniform solid disk and a uniform hoop are placed side by side at the top of an incline of height h. If they are released from rest and roll without slipping, which object reaches the bottom first? Verify you...
  44. S

    Analyzing Rolling Motion of a Thin String on a Disc

    A thin string has been wound around a homogenous circular disc A in such a way that the disc can oroll on a horiz0ontal surface. The mass of the disc is M and its radius is R. The string goes around a small frictionless pulley C at a height 2Rabove the horizontal table B. To the free end of teh...
  45. V

    Kinematics Rolling motion off a cliff

    So I'm sure most everyone has come across the problem where you have a smooth rolling object on an inclined plain that rolls off a roof or something and falls some distance x away from the roof. I can solve that because it usually gives me the distance along the incline and the angle of...
  46. A

    1st year problem. Rolling Motion.

    I am haveing trouble solving a problem that should be fiarly easy. I believe that i have all the components of the question togethor but i can't solve it. 1. If you have a cylinder and a sphere roll down a 3m long board at angle theta, and the time for the cylnder to reach the bottem is 2.4s...
  47. M

    Rolling Motion of a bowling ball

    How do I do this Problem?: A bowling ball is given an initial speed of 5m/s on an alley such that it slides initially without rolling. The coefficient of friction between the ball and the alley is 0.12. How far must the ball travel until pure rolling motion sets in? Any help would be...
  48. W

    Solve for Angular Displacement with Acceleration: Rolling Motion Help

    Hi, I am working on the following problem: As you drive down the road at 17 m/s you press on the gas pedal and speed up with a uniform acceleration of 1.12m/s2 for 0.65s. If the tires on your car have a radius of 33cm , what is their angular displacement during the period of accceleration...
  49. S

    What is the acceleration of the bowling ball in a subway car?

    A bowling ball sits on a level floor of a subway car. If the car has a horizontal acceleartion a, what is the acceleration of the ball wrt the ground? Ball rolls w/o slipping. The forces that act on the ball are its weight, a normal force, and static friction. The weight and normal offset...
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