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.
Hi guys,
Homework Statement
I'm trying to find the theoretical time it takes for a glue stick to roll down an inclined plane of 10 degrees. We then have to compare it to the practical value, which was 1.09 secs.(Average over 10 repetitions). The glue stick has a mass of 10g. The distance of...
Homework Statement
A hoop of mass ##m## and radius ##a## rolls without slipping inside a pipe of radius ##R## (the motion is 2D). Write down the kinetic and potential energy. Hence find the frequency of small oscillations about equilibrium.
Homework Equations
Moment of inertia of a hoop...
A ball is attached with a string on the side. When the string is pulled up, static friction accelerates the ball forward while the tension rotates the ball.
When a ball is placed on a incline with friction, is kinetic friction opposing the motion and giving the ball torque while gravity...
Hi,
The below questions are NOT HW questions, but I have a big exam coming and I would wholeheartedly appreciate some/any assistance with the following two issues, namely:
(1) Direction of static friction in case of rolloing without slipping
(2) Direction of α and VCM in case of rolling without...
It seems that I could have a solid cylinder roll down faster than a solid sphere if the center of the solid cylinder had a very dense material and then a less dense material towards the outside.
Imagine a set of train tracks. Now there is one bridge (a resistor) connecting the two rails in one spot. On a different spot, there is rolling axle that acts as another bridge and it makes good electrical connection with the rails creating a full rectangular circuit. This axle rolls at a...
Homework Statement
Roll a 6-sided die 5 times. Event X is when a 1,2,3 shows up. Event Y is when 4,5 show up. Show the joint PMF.
Homework Equations
The Attempt at a Solution
So... here is where I am at...
X~Bin(5,0.5) & Y~Bin(5,1/3)
P(X=x)=(5 C x)(.5^5) &...
Hello,
My problem refers to hard tyres, so assuming none or very little lateral deflection. For a particular tyre on a particular floor there is a rolling resistance against the movement when the tyre is rolling. In a simplified case the resistance can be approximated as a rolling resistance...
Homework Statement
A rigid ball of mass m = 6kg and radius R = .23 m is sitting on a table. The mass center and geometric center of the ball coincide, but the radius of gyration about its mass center is k = .19 m. The ball is initially at rest. There is a coefficient of friction μ = .435...
Hi everyone - quick question on something that's been bugging me. So, train wheels, which are solid steel, have incredibly low rolling resistance, an order of magnitude less than average car tires. This is because they don't bend significantly, so you're not wasting energy to heat as in the...
Freight train is more efficient than truck due to lower rolling resistance. And I wonder which one has lower rolling resistance, small diameter or larger one or it doesn't not depend on diameter at all? Both are steel wheel on steel rail.
Five standard 6-sided dice are rolled. What is the probability that at least 3 of them show a six?
I am surprised my answer is wrong.
First the total outcomes are 6x6x6x6x6=7776
Successful outcomes 10x6x6=360
There are 10 ways to choose 3 from 5 and then the remaining 2 can be any number...
Homework Statement
Homework Equations
The Attempt at a Solution
The force on the loop due to magnetic field in the direction normal to the incline is ##qvB##.
Balancing forces in the direction normal to the incline,
mg\cos\alpha=qvB+N
where ##N## is the normal reaction due to incline and v is...
We know that in real world scenarios, for rolling without slipping of bodies like sphere, dis, cylinder etc. there is a rolling resistance present. This rolling resistance comes from the fact that in actual situations bodies aren't perfectly rigid. So there is some compression at the point of...
Is friction always zero when pure rolling has begun? Or is it static? Is there a difference between saying static friction at the point of contact and zero friction at the point of contact at the time when pure rolling has begun? That is of course for a rough surface on which the object is rolling.
Homework Statement
A solid sphere of radius R is given a translation velocity vo on a rough surface of coefficient of kinetic friction=coefficient of static friction=μ. After what time does the sphere begin pure rolling? Also find the the angular velocity and linear velocity of the sphere at...
Homework Statement
This is a conceptual doubt.
"A sphere rolls without slipping moving with a constant speed on the fixed rough surface. Friction between the surface and the sphere is sufficient to prevent slipping."
What does it mean that friction is enough to prevent slipping? From what...
Hi all,
I have a question about how to analyze the problem of a ball rolling down an incline plane. Assuming there is friction, at each instant the ball swivels about a pivot point on the incline that is stationary due to static friction. We then would analyze the torques about this point...
Is frictional force necessary for rolling without slipping? If yes then does that mean that if we provide torque to a solid sphere on a frctionless surface will it nor rotate? I didn't understand that when does static frction arise and when does kinetic friction arise when a body is rolling...
What do we mean by the statement "Rolling with slipping"? I couldn't imagine this situation as a real life scenario.. I mean to say that if the body (say a solid sphere) is slipping/skidding then how can it rotate? If it will be rotating it won't be slipping/skidding. How can the two happen...
Hi all:
I have been wondering:
picture a cylinder sitting above a sheet of sand paper, assume static friction between the sheet of paper and the cylinder.
if i start pulling the sheet of paper at velocity v along a direction of rolling (to the left), the moment caused by static...
This is probably a silly question, but I want to make sure I get it right for a story I'm writing.
I want to roll an elongated spaceship "around" it's horizontal axis (as opposed to flipping it end over end). Is it equivalent to say "along" the horizontal axis?
In this case, I'm assuming...
Homework Statement
A cylinder rolls without slipping down a hill. It is released from height h. What is its speed when it come down? The cylinder mass may be completely concentrated on the radius R, which is the radius of the cylinder.
http://i.imgur.com/Ge3x1nu.png
The Attempt at a...
Homework Statement
A round cone A of mass ##m## and half-angle ##\alpha## rolls uniformly and without slipping along a round conical surface B so that its apex O remains stationary. The centre of gravity of the cone A is at the same level as point O and at a distance ##\ell## from it. The...
Hi PF.
I'm currently developing a 2D platform game that is significantly physics-based using the Box2D physics engine.
However, one of my main problems right now is that the main "character" of my game is a ball and unfortunately, Box2D does not support rolling friction. The result is that...
Homework Statement
Homework Equations
Wnon-conservative forces = ΔEnergy
The Attempt at a Solution
I understand that I am to solve for the D in Wnon-conservative forces since I know the friction force. I am just having trouble understanding what the initial/final kinetic...
Homework Statement
An experiment was done to test the validity of the equation a = 2/3 g sin∅ for a rolling cylinder. A hockey puck was rolled down a wooden ramp at 5 different inclination angles, and the time it took to roll down the length of the board was recorded. ∅ was found using...
Homework Statement
A solid sphere rolling on a rough horizontal surface with a linear speed ##v## collides elastically with a fixed smooth, vertical wall. Find the speed of the sphere after it has started pure rolling in backward direction.
Homework Equations
The Attempt at a...
Homework Statement
A certain die is weighted such that probabilities of showing a 1, 2, 3, 4, 5, and 6 are
(6/34),
(8/34),
(5/34),
(3/34),
(8/34),
and
(4/34)
A) If two such dice are thrown, and you are told that the sum of the two is 10 or larger. What is the probability that the...
Homework Statement
A cylinder of radius r, mass m, and rotational inertia 1/2mr2 slides without rolling along a flat, frictionless surface with speed v0. At time t = 0 the object enters a region with friction (with coefficients μk and μs), as shown above. Initially the cylinder slips...
Homework Statement
A solid disk of mass m and radius R rolls without slipping with a velocity v. Assuming it doesn't slip, how far vertically will it roll up an incline?
Homework Equations
I=0.5mr2
E=0.5Iω2
KE=0.5mv2
PE=mgh
The Attempt at a Solution
I'm thinking that we need to...
Homework Statement
Homework Equations
The Attempt at a Solution
My answer is a because for ball B it loses kinetic energy when it drops into the dip and comes back up.
I'm having a hard time picturing ball b when it goes down the dip.. does it drop down and then jumps up...
Hey guys, I've been thinking about inertia/forces for a test I have soon and I've been stumped by a question that the teacher gave us a while ago.
Suppose a football is rolling along the ground and you give it a swift kick in a direction perpendicular to its initial motion. In what direction...
Homework Statement
The mass of the ball: 136 G
Length of the slope that its sliding down: 132 Cm
Angle of the slope that its sliding down: 11,5228 °
All I have to do, is to find the velocity, and the acceleration of the ball. Though my teacher has given us no time at all for this project...
Homework Statement
I have a question from my homework. My homework is completed, but I've been running some thought experiments lately and I wish to conceptually discuss this.
The problem has to do with a hoop rolling down an inclined plane. I had to find the Normal Force using...
Here are the few equations i set up... which ultimately led to a wrong answer.
(In my solution, subscripts A refers to the ramp, B refers to the rolling pipe)
----------
I have a feeling that the acceleration if pipe A isn't simply downwards at 30deg.
Cos the ramp is rolling away, so...
Homework Statement
Homework Equations
The Attempt at a Solution
The change in velocity = a * change in ω
I think that makes sense since for pure rolling v = aω
16 marks like that?
Homework Statement
A ball of radius ro rolls on the inside of a track of radius Ro. If the ball starts from rest at the vertical edge of the track, what will be its speed when it reaches the lowest point of the track, rolling without slipping?
Included below is a link to the diagram...
I've been having trouble with this topic for a while now. I've re-read the section dozens of times now, but I'm still not exactly clear and I was hoping for clarification on a couple of things.
In a system of particles, I can see intuitively how the velocity of a particular particle will be the...
Homework Statement
A spherical ball of mass m and radius r rolls without slipping on a rough concave surface of large radius R .It makes small oscillations about the lowest point.Find the time period.
Ans : 2∏\sqrt\frac{7(R-r)}{5g}
Homework Equations
The Attempt at a Solution...
Hi, I'm trying to find the Acceleration of a ball rolling down on a parabola.
If I could find it, then I could integrate it twice and find it's parametric equation given by the time.
How could I find this?
I tried a few things, but nothing that made any sense.
If someone could give me a hint...
My ultimate goal is to spec a motor for a shop tool. It is a stand to rotate a glorified pipe. The pipes are quite large (up to 19,000lbs). The pipe will sit on four wheels. Two of the wheels are motorized. I have a good idea of the torque/hp needed to accelerate to the desired angular velocity...
Homework Statement
I have math experiment where I roll a pair of honest dice 20 times.
The results are:
2,3,4,4,5,5,6,6,6,7,7,7,7,7,9,9,9,10,10,11
write a frequency table of the outcome of the dice roll with respect to size:
2,3,4,5,6,7,8,9,10,11,12
Firstly there must 36...
I'm trying to get the position vector of the offset mass relative to the inertial frame of reference. Do I account for the fact that the disk has rolled a little bit with respect to the inertial frame of reference? With that, I have
r,vector = d n1 + R n2 + R/2 er = R*theta n1 + R n2 + R/2 er...
Hi,
Consider a ball rolling upward without slipping on an inclined plane. What is the direction of the force of static friction?
Let me explain what confuses me. I know that the friction opposes the tendency of the motion. If we consider the whole motion of the ball as upward, then the...
Homework Statement
This is regarding the following problem: http://s24.postimg.org/bmaa4a65h/sphere_in_bowl.png
Homework Equations
I will be referring to this drawing: http://s22.postimg.org/6zl9mw9zj/drawin.png
The Attempt at a Solution
Let me just show first how I got my answer and I'll...