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.
Homework Statement
a 76 kg boulder is rolling horizontally at a top of a vertical cliff that is 20m above the surface of a lake. the top of the vertical face of a dam is located 100 m from the foot of the cliff, with the top of the dam level with the surface of the water in the lake. a level...
Homework Statement
A cylinder with mass m and radius a rolls down a fixed cylinder with radius b. Let \theta be the angle between the plane containing the axis of each cylinder and the vertical. Find the normal component of the reaction force exerted on the rolling cylinder.
Homework...
Hello.
I'm trying to find the torque required of an electric vehicle to pull a 1000kg trolley on four Nylon Wheels on smooth concrete. The trolley fully supports its own weight. The vehicle has 2 rubber drive wheels of Radius( r = .125m). Now I'm not sure if am on the right track because i...
Homework Statement
A uniform ball of mass M and raduis a can roll without slipping on the rough outer surface of a fixed sphere of raduis b and centre O. Initially the ball is at rest at the highest point of the phere when it is slightly disturbed . Find the speed of the center the G of the...
Homework Statement
Let there be two spheres, of equal radius but unknown masses (mass isn't important).
Both move down a ramp of angle \theta, where \theta can be any angle but 90 deg. or 0 deg.
The first sphere slides down the ramp with no (negligible) friction. This sphere does...
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...
Homework Statement
A cylinder, radius R, mass M and moment of inertia I, is rolling on a horizontal surface without slipping and a constant force F is exerted on the center of the cylinder horizontally to the right. Try to find the friction by solving the Lagrangian equation.
2. The...
Homework Statement
"Suppose the sloping surface was very slippery so no rolling occurs (the can slides). Would the can reach the bottom sooner or later compared with the rolling motion? Explain the difference"
I don't know if its relevant, but the slope was 4cm at the high end, and 1.5...
Greetings to all
I apologise if this has already come up before, I found many related topics on these forums but nothing dealing with my specific problem (providing it is due to a physics error and not a programming one).
I'm currently in the midst of programming the physics part of a...
Homework Statement
a small ball slides , with constant speed (a\theta tangential acceleration = 0) , around a horizontal circle at height h inside a firctionless, hemispherical bowl of radius R.
derive a formula for the balls angular velocity \omega in terms of the radius of the radius of the...
Homework Statement
A ball rolls up a straight incline. The dots in the diagram represent the position of the ball every 4 seconds.
(The fourth dot is not intended to represent the turnaround point; the ball might still be on the way up at that
point.) The instantaneous velocities at the...
Homework Statement
A ball rolls up a straight incline. The dots in the diagram represent the position of the ball every 4 seconds.
(The fourth dot is not intended to represent the turnaround point; the ball might still be on the way up at that
point.) The instantaneous velocities at the...
Homework Statement
Not a problem but an experiment were I have not been told what I need to calculate.
I have a trolley rolling down an inclined plane. We recorded the speed(light gates) at two different points and all distances involved(height of plane, distance between gates etc). We did...
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...
Dear All,
I have learned that if a wheel is rolling without slipping, then the velocity of point of contact of a wheel with respect to the ground is zero instantaneously.
However, I am having some problems while trying to understand that.
We can express the point of contact's velocity...
Hi All,
I'm trying to figure out how to model a rolling ball in the x y plane.
I've started with the basic equation of motion with constant acceleration
d = v_{}0t + 1/2at^{}2
v_{}0 is the initial velocity
a is acceleration
t is time
Assume that v is a vector at an angle \alpha...
Homework Statement
A uniform hollow spherical ball of mass 1.75kg and radius 40.0cm rolls without slipping up a ramp that rises 30 degrees above the horizontal. The speed of the ball at the base of the ramp is 2.63m/s. while the ball is moving up the ramp, find the acceleration of its center...
Homework Statement
A small, solid sphere of mass 0.6kg and radius 27 cm rolls without slipping along the track consisting of slope (at an angle of 60degrees from horizontal) and loop-the-loop with radius 2.65m at the end of the slope. It starts from rest near the top of the track at a height...
Homework Statement
A toy car has a total mass of 50 g, and rolls on freely spinning wheels, each of which can be modeled as a uniform disk of mass 1 g, and radius 2mm. What is the acceleration, a, of this toy car when it rolls without slipping down a ramp tilted at an angle of 20 degrees to...
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...
Hello:
In my readings a question has come up in my mind about a ball that is rolling. Say you have a pool ball on a billiards table and you examine it immediately after impact. It's going to be sliding along the table. But at some point, it's going to stop sliding and (ideally) start rolling...
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...
hi there!
I considered the following problem:
a ball of radius R on a horizontal plain is at first in rest. Then it receives a horizontal force for a very short time at a point placed 1/3R from the plain and the ball starts moving with initial velocity v_0. There is also a friction when...
Homework Statement
See post #3 Assume the YoYo is a solid cylinder with mass M and radius R for all parts!
Homework Equations
Lots?
The Attempt at a Solution
Part A - Find the moment of inertia about the center of mass and the point of contact with the ground:
ICOM = 1/2 MR2
IIPoC = 1/2...
HELP!A rolling without slipping problem
Homework Statement
A solid cylinder of radius R and mass M has a string wrapped around it and is placed on its side on a horizontal surface. The free end of the string is pulled horizontally with a force F as shown in the figure. As the string unwraps...
The problem is modeling a solid ball or radius R rolling down an incline of angle Theta. Note that I am an Electrical Engineer who is somewhat flaky with rotational concepts (but not completely useless :p). If the ball was rolling down a road (or any solid, flat surface), I get the following...
Consider a ball rolling on a horizontal plane where friction is present. The forces acting on the ball are mg, friction at the contact and the normal force. This friction acts opposite to the direction of velocity. That should provide a clockwise torque and hence increase the angular velocity of...
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...
Homework Statement
A uniform cylinder of mass m of radius r(smaller) rolls on a cylindrical surface of radius R(larger). At a certain instant, the line OC has an angular velocity \omega and angular acceleration \alpha.
http://img82.imageshack.us/img82/5380/cylinerssm0.jpg
Find
a)...
Homework Statement
A solid sphere has a mass of 1.0 kg. It is rolling at a translational speed of 10 m/s. What is the total energy of the rolling sphere?
I think I got the problem but I'm not sure I went about it the right way.
Homework Equations
I = (2/5)mr^2
KE_rot = (1/2)Iw^2
KE =...
A uniform, spherical bowling ball of mass m and radius R is projected horizontally along the
floor at an initial velocity v0 = 6.00 m/s. The ball is not rotating initially, so w0 = 0. It
picks up rotation due to (kinetic) friction as it initially slips along the floor. The coefficient of...
i have a problem regarding rolling wheels. ihave a double wheel rim connected by spokes, which is in perfect balance, with two baskets hanging between them, on opposite sides of the wheel, such that when a weight is added to the top basket the wheel will rotate, dropping the basket at the bottom...
Hey guys!
I'm doing my B.S thesis (Mech. Eng.) and I've come across the problem of a rolling disk with friction. Imagine a disk in real world rolling on a flat surface with no external force or torque applied to it except for the interaction of the surface (Normal, friction, etc.).
Now...
Hello guys,
I would like to help me with rolling friction on a car(i am building a project that simulates the forces
applied to a vehicle when it moves on a straight road http://rapidshare.de/files/40862186/Vehicle_Sim.zip.html).
So:
Engine has a torque at some RPM,and the torque goes...
Homework Statement
A basketball (which can be closely modeled as a hollow spherical shell) rolls down a mountainside into a valley and then up the opposite side, starting from rest at a height H0 above the bottom. In the figure, the rough part of the terrain prevents slipping while the...
Homework Statement
A ball has a diameter of 25.4 cm and a mass of 566 g. It can be approximated as a hollow spherical shell. Starting at rest, how long will it take to roll 10 m down an an incline of 30 degrees if it doesn't slip?
Homework Equations
Energy conservation
I = 2/3 mr^2...
A potter has a stone disk of radius 0.483 m and mass 101 kg rotating at 71.9 rev/min. The potter stops the wheel in 6.54 seconds by applying a wet towel against the rim with a radially inward force of 103 N. Find the effective coefficient of kinetic friction between the whell and the wet towel...
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...
1. Under all ordinary conditions, would a ball released from rest start rolling down a frictionless inclined plane with just the force of gravity pulling it down? Or is it really just going to slide down?
Now let's suppose a gigantic ball released on the slope of an enormous frictionless...
Homework Statement
A disk has mass 3kg and outer radius 50 cm with a radial mass distribution (which may not be uniform) so that its moment of inertia is (2/7)mR^2. The disk is given a hard kick (impulse) along a horizontal surface at time t0. The kicking force acts along a horizontal line...
A ball of mass 2.10 kg and radius 0.145 m is released from rest on a plane inclined at an angle theta=38.0 degrees with respect to the horizontal. How fast is the ball moving (in m/s) after it has rolled a distance d=1.50 m? Assume that the ball rolls without slipping, and that its moment of...
Edit: The title is misleading because I initially was going to ask a different question.
Homework Statement
A singly charged ion of mass m is accelerated from rest by a potential difference ΔV. It is then deflected by a uniform magnetic field (perpendicular to the ion's velocity) into a...
Homework Statement
If you start a penny rolling on a table with care, you can make it roll in a circle. The coin leans inward with its axis tilted. The radius of the coin is r, the radius of the circular path it follows is R, and velocity is v. Assuming that the coin does not slip, find the...
Homework Statement
Take down as positive. A car is parked near a cliff overlooking the ocean on an incline that makes an angle of 10.5 degrees 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...
Homework Statement
An Airbus A320 jetliner has a takeoff mass of 75,000 kg. It reaches its takeoff speed of 82 m/s in 35s.
Find the Thrust of the engines, don't worry about air resistance, but rolling friction is substantial.
Homework Equations
Fnet=mass*acceleration
a=(82/35)...
Homework Statement
a. A 49,000 kg locomotive is traveling at 11 m/s when its engine and brakes both fail. How far will the locomotive roll before it comes to a stop?
_____m
b. Determine the stopping distance if the locomotive had the same initial velocity but was "low on diesel" so...
1) A balanced die is tosssed six times, and the number on the uppermost face is recorded each time. What is the probability that the numbers recorded are 1, 2, 3, 4, 5, and 6 in any order?
My attempted answer is (6!)/(6^6), is it correct?
2) Suppose a die has been altered so that the...
I'm driven crazy by this question these days. so here it goes.
Consider a ball sliding on a frictionless surface with some velocity U. If it encounters a surface with friction after some time, then it starts rolling (thats what my intuition says). Meaning that a new rotation component has been...
Homework Statement
A think cylindrical shell and a solid cylinder have the same mass and radius. The two are released side by side and roll down, w/o slipping, from the top of an inclined plane that is 4.9m above the ground.
When the first object reaches the bottom, what is the height above...
Q: A ball is at rest on an inclined plane. It begins to roll down with an acceleration of 2 m/s^2. How long does it take the ball to roll 50 m?
This is my work:
find time using, s = ut + 1/2 a t^2
t = sqrt(2s/a)
Plug in the s = 50 and a = 2
Am I right?
Thanks a lot.