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.
Cylinders rolling down inclines are a common demo.
But how do you model the movement of a sphere rolling within a rolling cylinder?
I teaching a physics class and this question came up and my dynamics math is a little rusty.
But I haven't found anything like this in any book or online.
There's...
By solving conservation of energy, I was able to find the linear velocity which is
[10g(H-R-Rsin(theta))/7]^½ and by differentiating this with respect to "t", I arrived at the tangential acceleration value of -(5gcos(theta))/7 and found it to be in agreement with the solution provided in the...
I know the ans comes out to be mgsintheeta/3 by using f=ma and the torque eqn but my question is as stated in the question the cylinder is in pure rolling hence friction should only try to oppose mgsintheeta so that the accelration does not change hence v remains equal to rw so why is the ans...
Problem Statement: Let there be a ring of mass m and radius r. Let 3 masses be attached to the ring and named as O,P and Q. Mass of O and Q is 2m and mass of p is M. The angle between 2 masses is 15 degrees as shown in the figure.
Find the maximum velocity the ring must roll so that it doesn't...
Homework Statement
In the picture ,problem 8.29
Homework Equations
Energy conservation ,velocity relation ,momentum
The Attempt at a Solution
First i defined the speed of the body relative to the ground as Vb and speed of plane relative to the ground as Vp.
From momentum ,VbcosΘ=-Vp .From the...
I have been reading quite a lot about the Physics behind car dynamics and I have gotten to a point which keeps confusing me, namely - brake locking.
I understand brake locking as the situation when the wheels of the car do not rotate anymore but the car is still moving - this causes the tires...
Homework Statement
Side by side on the top of an incline plan with height=2 meters a cylinder (Ic= MR^2/2) and a sphere (Ie=2MR^2/5) with equal radius, that come down to the base, rolling without slipping. Mass of the cylinder = 2.0 kg; Mass of a sphere=4.0 kg.
Homework Equations
$$K_r= 1/2...
Homework Statement
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A wheel, of radius 200mm, rolls over the top of a hill with a speed of 20m/s and negligible friction losses. (I = 1/2mr^2)
Homework Equations
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Find the speed of the wheel when it is 10m below the top.
The Attempt at a Solution
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mgh = 1/2mv^2 + 1/2IW^2
W=...
Hi there! I chanced upon this problem whilst trying to brush up my Classical Mech knowledge and found it confusing. Hope someone out there can provide an insight!
Homework Statement
A bowling ball of mass m and radius R sits on the smooth floor of a subway car. If the car has a horizontal...
Hello, this is my first time on this site as a member, but I have found it very helpful all year. In my physics class we are trying to come up with a way to get a can to roll down an incline as fast as possible. We have to empty out the food from the can, then do whatever we can to it to make it...
Homework Statement
A cart with mass M has four wheels (idealized as uniform discs), each of radius r and mass m, arranged symmetrically with respect to the cart. Find the acceleration of the cart when a horizontal force F is applied on it. There is no slipping between the wheels and the...
Homework Statement
With the equations of motion in polar coordinates given by ##r(t)=pcos{kt^2}, φ(t)=kt^2## determine the velocity intensity of a point ##M## on the circumference of a cylinder which is rolling without friction on a horizontal plane at time ##t## is the velocity of the center...
Im starting to learn about vehicle dynamics by watching video lectures here , and also reading the books by Gillepsie and Jazar. I´ve got a fundamental question about the FBD of the vehicle.
According to Gillepsie :http://imgur.com/a/lGXxw
http://imgur.com/a/lGXxw
The vehicle is...
Hi! Well, I'm programming a vehicle's physics, and I have trouble finding a way to calculate Rolling resistance, though i searched a lot. I already have the Traction Force and the Drag Force, but now I need Rolling Resistance. The best thing i found is that Froll = Croll * P, where Croll is the...
This isn't about a specific physics problem, but rather a question:
Given I have a ball or cylinder rolling smoothly along some path, is it generally true that mechanical energy is conserved?
I.e. if ##E_mech = K+U = K_{trans} + K_{rot} + U##, then ##\Delta E_mech = 0##?
I have been able to...
Homework Statement
(i) Suppose there's an object rolling without slipping at any surface.
(ii) Now, let's say a disk is rolling and slipping toward the +x direction
2. The attempt at a solution
(i) If the surface is horizontal then it won't apply any friction force on the object regardless on...
Homework Statement
There are two problems:
(A) Consider two identical billiard balls (spheres), each of mass M and radius R. One is stationary (ball 2) and the other rolls on a horizontal surface without slipping, with a horizontal speed v (ball 1).
Assume that all the frictional forces are...
Homework Statement
A solid sphere is rolling without slipping on rough ground with an angular velocity w and linear velocity v. It collides elastically with an another identical sphere at rest. Radius of each sphere is R and mass m. What is the linear velocity of the first sphere after it...
Homework Statement
source:http://www.wired.com/2014/07/a-rolling-object-accelerating-down-an-incline/
For a ball rolling on an incline, I know how to calculate the acceleration. However, I am quite confused about a situation. What if static friction acting on the ball is equal to the...
Homework Statement
A solid sphere of radius R is set into motion on a rough horizontal surface with a linear speed v0 in forward direction and angular speed ω0##=\frac{v_0}{2R}## in counter clockwise direction. Find time after which pure rolling starts.
Homework Equations
For pure rolling...
Dear Physics lover friends,
I am in the middle of something and I would like to ask a question on how to solve this branch wheeled problem.
The yellow lines are the branches, they have one wheels on them and the wheels are on a circular path.
I would like to know how much the normal force A...
Hello,
1. Homework Statement
A spherical continuous ball is sliding with a constant velocity v along a frictionless lane. Thereafter it enters an inclined surface (the angle between the surface and the horizontal plane is α) with the coeﬃcient of friction µ between the ball and the surface...
Hey all,
I'm stuck on this problem and not sure how to proceed/if I'm in the right direction.
Problem: One reference frame N sits at the origin (inertial frame) while another frame, B, describes a disk rolling on a circular ring about the other frame. Picture below
(A) find the direction...
Homework Statement
I'm doing a coursework where I must find the angular acceleration of a rolling tin can using theoretical values. I have its mass and radius. I actually have experimental data so i have access to the actual values of angular velocity and angular acceleration, as well as time...
Hi I am doing an assignment where I roll a tin can filled with car oil. This will affect its rolling because it distorts its centre of mass, resulting in an awkward rolling motion. I have already done the experiment, the first revolution is the slowest one by a lot because it slows down a lot...
when a sphere starts moving with initial velocity ##v_0## and zero angular velocity in a plane surface having friction, then first it will start rotating till it starts pure rolling. that is, its velocity of centre of mass will decrease due to backward friction and angular velocity will increase...
Homework Statement
A yo-yo is pulled with a constant tension T. The string is horizontal and parallel to the table and unwinding from the bottom of the spool, as shown. The yo-yo's outer radius is R and the spool radius is r. The mass of the yo-yo is m and the moment of inertia of the yo-yo...