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.
My Son asked me a question, I am not sure how to answer it.
It feels easier to push or roll a heavy ball up a hill than it is to pick it up and carry it up the same hill.
The ball has the same potential energy at the top of the hill no matter how it got there so it would appear to be...
Homework Statement
A right triangular prism ABD with inclination angle 30degrees and mass m can slide without friction along smooth horizontal surface. A uniform solid cylinder of mass m rolls down the inclined surface AB without friction. If both cylinder and prism are at rest...
Hi,
This has been bugging me for a little while now. Imagine a ball is rolling along on a rough surface without slipping. Under ideal conditions it will just continue rolling indefinitely right?
However, if you were to draw a free body diagram the normal and gravitational force would...
Homework Statement
A car is parked near a cliff overlooking the
ocean on an incline that makes an angle of
14 with the horizontal. The negligent driver
leaves the car in neutral, and the emergency
brakes are defective. The car rolls from rest
down the incline and has a velocity 5 m/s...
Homework Statement
There is a tube attached to a board in a fashion that a ball can be dropped in the top and the tube curves to the right 90°. If a ball of mass 7.6g is dropped into the top of the tube, what is the minimum height the exit point of the tube needs to be in order for the ball to...
(Note to the mods:
This post is a link to an art piece concerning the Higgs boson, and not an actual question. I looked though the boards, trying to figure out the appropriate place to post it, and this board seemed most likely. If it doesn't belong on this board, please forgive me and move it...
Homework Statement
At what speed should a coin of radius a and mass m roll to stay upright? Assume the coin is uniform, a thin disk, almost upright, and rolling on a perfectly rough horizontal surface, on the surface of the earth.
The Attempt at a Solution
I've found a solution using the...
We are given with an hollow thin cylinder that has a mass of M and radius R, and a full cylinder that has a mass of m and radius r. The full cylinder is glued to the bottom of the hollow cylinder
(As in the picture - ignore the speed v0 that is drawn in the picture) and now the hollow cylinder...
Hello Forum,
Consider a rigid disk that is rotating on a surface. If the surface is elastic but not symmetric, the rotating disk will eventually slow down.
If the surface was perfectly and symmetrically elastic the object will continue to rotate (the front deformation of the surface would...
Hi everyone, good day. this might be a simple question, but I need someone to check my answer.
A disk and a hoop, of same mass and same diameter, is first giving a torque (same amount of torque for both) then the torque is removed (the torque is acting on them for the exact same period of...
Hi everyone, Good day.
for the effect of friction on wheel (all the questions are based on rolling without sliding), i know that in the case of uniform rolling, there will be no friction on the wheel. while for accelerating or decelerating case, there will be friction on the wheel (but in...
First I want to introduce a exercise I tried to solve, and then the doubt I have at the final resolution.
"In a slope with θ angle to the horizontal plane, a homogen ball with radius R and mass m roll down without slipping. Calculate the friction force."
Force equilibrium ma = mg sinθ - Ff...
If we had a cylinder rolling down a ramp, with scalar friction coefficient us and kinetic friction coefficient uc, and we assume for example that the inclination of the ramp is enough to make the cylinder reach the acceleration needed to exceed the scalar friction of rolling. It means that the...
Hi
Can anyone please clarify the following?
Let there by a rolling cylinder on an inclined plane. Let the solid cylinder(with Center O) on the inclined plane has Center of gravity at a distance 'c' slightly above O. If the cylinder is displaced slightly through an angle θ then
[Let N =...
Homework Statement
A car on the frictionless track starts from rest at height h. The tracks valley and hill
consists of a circular-shaped segments of radius R.
What is the maximum height h from which the car can start so as not to fly off the track when going over the hill?
Give your...
Homework Statement
A 1500kg car traveling at 10m/s suddenly runs out of gas while approaching a valley.
The car is 10m above the valley floor when it starts to coast down the valley.
the gas station is 15meters above the valley floor on the other side.
How fast will the car be going...
Homework Statement
A ball with mass 1.0 kg and radius 0.20m rolls without slipping along level ground with a speed of 10 m/s. The ball then rolls up an incline reaching a maximum vertical height of 8.0 m. What is the moment of inertia of the ball? (Do not assume the ball is a uniform sphere)...
Homework Statement
I need to find the horizontal velocity of an object on a ramp where the first height is 5.0m and the second height is 3.0m? I also need to find the time it takes to fall from the ramp, and the distance it falls away from the ramp. I am only given the two heights, an initial...
Homework Statement
Determine an equation for rolling resistance for a wheeled vehicle @20 mph.
Homework Equations
(1) Drr = Crr * g * m * V
The Attempt at a Solution
(2) Drr = Crr * g * m
My real question: is velocity a valid part of...
Greetings:
I want to make a stylus for a capacitive touchscreen which has a rolling ball at the end - like a ballpoint pen. I would like to make it myself in order to get the right size, rather than try and modify existing styluses on the market.
I would really appreciate any pointers as to...
hey i had a bizarre thought, what if there is a road made with a very smooth friction less surface and a normal asphalt road, arranged alternatively, such that , half the time spend by the tire in one rotation is placed on the smooth side and the other half on the rough side, such that the tire...
Consider a sphere and a semicircle with radii r and R respectively.(R>>r)
The sphere has mass m.Imagine we place it in the semicircle and let it rotate in it.
Let's take the z axis the line which passing through the center of the semicircle and the bottom of the semicircle with the origin at...
Can anyone help me with this one please...
If i roll a dice 100 times and number 6 comes out on 14 occassions (14%) what would have been the probability of number 6 being rolled 4 times in a row? (as a percentage?)
If someone would be so kind to tell me how to calculate this in simple terms...
Hi. I'm taking a look at this problem:
And my doubt is with step 2 when he calculates the torque. He just says it is Fd. But...why? F only has a component which effectivly does torque.
Thanks
Hi all. I'm struggling to understand how and where the friction forces that appear on the motion of a wheel on a flat surface, but I don't know if I understand it properly. I hope that you can help me. I try to describe the problem as follows.
When a wheel is not moving, and there are no...
Hi,
I have been trying to find some information on the forces acting on the wheel when the vehicle is moving but I am a little bit confused. I would be grateful if someone explain me the basic principles.
What I understood so far is;
(assuming front wheel drive)
* when the car is...
Homework Statement
I think I have too many equations for unknowns for rolling without slipping. Suppose a wheel is pushed and left rolling along the ground without slipping.
Homework Equations
T = I*alpha, where alpha is the rotation about the wheel's centroid and I is the moment of...
I am really confused as to how to determine the direction of friction acting on a rolling object. Could someone help clarify how to determine the direction of friction? ANy help is appreciated ;)
Hi,
So I've built an electronic die that generates a pseudo-random number from 1 to 6 each time a push-button is let go of. I use 7 LEDs as a display, representing the dots on the faces of a die. A shift register connected to an oscillator results in a ripple counter that counts from 1 to 6...
The easiest way I can explain this is russian roulette. You have a six-sided die, and I need to find out the probability of the other person rolling a 6 before me, or dying in russian roulette with a 6-chamber revolver.
I know it's different depending on who goes first, so for my example, I...
I'm calculating the rolling resistance and air drag for a 60,000 lb truck. I used a Cd=0.7 for drag coefficient; 6 m2 for frontal area; and a rolling coefficient of Cr=.008; density of air=1.3 kg/m3.
I get a force from rolling resistance of 2142 N (Cr*mass*g). I get a force from air drag at 35...
Homework Statement
Hello Physics World,
This is a question that was presented in my High School Science Challenge by a teacher. It is sort of a brain teaser and we will be told the answer to it by next week. However, I was wanting to know your input.
So, looking at the image above...
Homework Statement
I am teaching a class where we are trying to find the K of I=1/2Kmr^2 from rolling a very thin cylinder down a ramp.
Homework Equations
Linear Forces: mgsinθ-F(friction)=ma
angular forces: τ=Iα where τ=F(friction)r, I=Kmr^2 and a=αr
distance=1/2*a*t^2 since the...
I'm looking over my notes here, we have a rolling disk down an incline plane and my goal is to find its acceleration in terms of its moment of inertia
My dilemma is, when finding the torque, I look at all 3 of the forces influencing it (normal, gravity, and the f_s). The n goes through the...
Homework Statement
EDIT: A solid homegeneous cylinder of mass M and radius R is moving on a surface with a coefficient of kinetic friction μ(k).
At t=0 the motion of the cylinder is purely translational with a velocity v(0) that is parallel to the surface and perpendicular to the central axis...
A disk with mass m and radius R is rolling down a hill with no slipping, until it reaches a wall and then stops:
I want to write a set of equations describing the position cordinates x and y of the disk's center of mass (point A) and the cordinates for point B.
mgsin(theta)=ma ->...
Homework Statement
Two uniform solid spheres, each with mass 0.862 and radius 8.00×10−2 , are connected by a short, light rod that is along a diameter of each sphere and are at rest on a horizontal tabletop. A spring with force constant 164 has one end attached to the wall and the other end...
I know how to calculate the probability of getting a 1 and then 2 or 1 and 1 and etc, that's just 1/6 * 1/6
Now what if I ask, what is the chance of getting a 6 from 3 rolls? Let's say I roll the dice 3 times and all I want is just a 6 from anyone of these roll? I just want one 6 from any...
Homework Statement
A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0 above the horizontal. After it has rolled 4.20 m along the ramp, the magnitude of its linear acceleration is closest to
Homework Equations
The Attempt at a Solution...
Hi all, this is my first post on Physics forums so I apologise in advance if I have posted in the wrong section etc. This is something that I have been trying to figure out for nearly a week now! I have modeled a vehicle in Solidworks, specifically an external roll cage, and hope to conduct a...
Homework Statement
A sphere rolling with an initial velocity of 30 ft/s starts up a plane inclined at an angle of 30o with the horizontal as shown. How far will it roll up the plane before it rolls back down?
Homework Equations
T_1+V_1=T_2+V_2
The Attempt at a Solution
We are...
Hypothetically, if I had a sphere and a block (of the same mass and material (hence the same coefficients of static friction for both interfaces) both stationary on a surface, they would require the same force to initiate motion?
Once moving, a coefficient of sliding friction is employed in...
Homework Statement
A solid homogeneous cylinder of mass M and radius R is moving on a surface with a coefficient of kinetic friction μk. At t=0 the motion f the cylinder is purely translational with a velocity v0 that is parallel to the surface and perpendicular to the central axis of the...
A uniform solid cylinder of mass M and radius R is at rest on a slab of mass m, which in turn rests on a horizontal, frictionless table. If a horizontal force F is applied to the slab, it accelerates and the cylinder rolls without slipping. Find the acceleration of the slab in terms of M, R, and...
My zipline is 200 feet long built with 7/16" Stainless Steel Cable. Would 3/8" cable result in a faster ride with less noise from the trolley due to significantly less surface area for friction?
Homework Statement
What is the probability of 4 independent dice summing to 20 or more?
Homework Equations
N/A
The Attempt at a Solution
I am not too sure how to approach this in an exam.
I have attempted to do it this way but it would be easy to miss out a term:
(I have put...
For hollow sphere rolling up incline:
I know that the kinetic friction will equal 2/3 acceleration since:
μgcosθ=2/3a
acceleration = 3/5gsinθ
so...kinetic friction = 2/5gsinθ
But how I do calculate the force of static friction??
Homework Statement
A pipe(thin ring)has a mass of 500kg and radius of 0.5m and rolls without slipping down a 300kg ramp. If the ramp is free to move horizontally(frictionless, determine the acceleration of the ramp. (angle of ramp is 30 degrees)
Homework Equations
Fs (static friction) =...
Hi,
I have another query related to rolling motion.
Lets say a disc is rolling purely with a velocity vo (this being the vcom).
It encounters a step.lets say that the step has a height h, where h < r, i.e., the step has a height less than that of the height of the center of the disc. SO...
Homework Statement
A 3.0kg solid cylinder (radius=.15m, length=.7m) is released from rest at a top of a ramp and allowed to roll without slipping. The ramp is .9m high and 5m long. Find the rotational and translational kinetic energy.
Homework Equations
krot=1/2Iw^2
Ktrans=1/2mv^2...