Rolling with and without slipping

In summary, rolling with and without slipping refer to two different types of motion for a rolling object. Friction plays an important role in both cases, as it helps maintain the rolling motion without slipping or can hinder it. The ability of an object to roll without slipping is affected by factors such as shape, size, and surface. The velocity of an object rolling without slipping can be calculated using the formula v = ωr. An object can roll without slipping on an inclined plane as long as the forces are balanced and the friction is enough to prevent slipping. The angle of the incline, mass, and shape of the object can affect this ability.
  • #1
Benny
584
0
Hi, I don't understand the difference between rolling with and without slipping. To put my question into some kind of context, consider a ball of radius r which rolls to the right along the x (horizontal) axis. The ball is traveling at a constant velocity v and continues rolling until it reaches a curved hill, eventually stopping at some distance H above the x-axis. If there is no friction between the x-axis and the ball then H can be found by solving (1/2)mv^2 + (1/2)Iw^2 = mgH...(1).

That is assuming that there is no 'slipping.' But what does slipping actually mean in this context? I was told that if there was 'slipping' then the value of H would be less than that obtained by solving equation (1). So if there is no slipping then does that mean that there cannot be any friction? It's all quite confusing to me. In particular, I don't understand the following means.

Let G be the COG of the ball which is rolling. Let point A be the point of contact between the ball and the x-axis (as a visual aid, the line segment AG is perpendicular to the x-axis). I vaguely remember certain consequences of slipping and no slipping in this situation but I'm not really sure. If there is slipping (or no slipping), then can something be said about the relative velocity of the points A and G?

Any help would be great thanks.
 
Physics news on Phys.org
  • #2
"Rolling without slipping" means that the point-of-contact has an instantaneous velocity of zero. There is no sliding there... hence no sliding friction.

G, traveling with constant velocity, is the green line
B (in blue) is the rotation of a point around the wheel axis--that point is initially in contact with the ground
A (in red) is the superposition of the two motions...
[tex] \]
\unitlength 0.02mm
\begin{picture}(4000,3000)(0,0)
\textcolor{red}{
\qbezier(6110,3268)(6230,3269)(6230,3269)
\qbezier(5998,3258)(6110,3268)(6110,3268)
\qbezier(5881,3233)(5998,3258)(5998,3258)
\qbezier(5771,3191)(5881,3233)(5881,3233)
\qbezier(5648,3121)(5771,3191)(5771,3191)
\qbezier(5541,3042)(5648,3121)(5648,3121)
\qbezier(5425,2941)(5541,3042)(5541,3042)
\qbezier(5307,2831)(5425,2941)(5425,2941)
\qbezier(5193,2723)(5307,2831)(5307,2831)
\qbezier(5073,2620)(5193,2723)(5193,2723)
\qbezier(4959,2537)(5073,2620)(5073,2620)
\qbezier(4843,2471)(4959,2537)(4959,2537)
\qbezier(4731,2428)(4843,2471)(4843,2471)
\qbezier(4613,2403)(4731,2428)(4731,2428)
\qbezier(4505,2394)(4613,2403)(4613,2403)
\qbezier(4385,2392)(4505,2394)(4505,2394)
\qbezier(4273,2391)(4385,2392)(4385,2392)
\qbezier(4148,2381)(4273,2391)(4273,2391)
\qbezier(4036,2356)(4148,2381)(4148,2381)
\qbezier(3920,2312)(4036,2356)(4036,2356)
\qbezier(3801,2244)(3920,2312)(3920,2312)
\qbezier(3687,2158)(3801,2244)(3801,2244)
\qbezier(3580,2066)(3687,2158)(3687,2158)
\qbezier(3458,1952)(3580,2066)(3580,2066)
\qbezier(3341,1841)(3458,1952)(3458,1952)
\qbezier(3232,1747)(3341,1841)(3341,1841)
\qbezier(3113,1660)(3232,1747)(3232,1747)
\qbezier(2999,1595)(3113,1660)(3113,1660)
\qbezier(2880,1550)(2999,1595)(2999,1595)
\qbezier(2771,1527)(2880,1550)(2880,1550)
\qbezier(2648,1517)(2771,1527)(2771,1527)
\qbezier(2542,1516)(2648,1517)(2648,1517)
\qbezier(2417,1514)(2542,1516)(2542,1516)
\qbezier(2312,1506)(2417,1514)(2417,1514)
\qbezier(2197,1482)(2312,1506)(2312,1506)
\qbezier(2077,1436)(2197,1482)(2197,1482)
\qbezier(1957,1368)(2077,1436)(2077,1436)
\qbezier(1851,1290)(1957,1368)(1957,1368)
\qbezier(1731,1186)(1851,1290)(1851,1290)
\qbezier(1614,1076)(1731,1186)(1731,1186)
\qbezier(1496,966)(1614,1076)(1614,1076)
\qbezier(1383,868)(1496,966)(1496,966)
\qbezier(1273,787)(1383,868)(1383,868)
\qbezier(1155,719)(1273,787)(1273,787)
\qbezier(1036,674)(1155,719)(1155,719)
\qbezier(918,649)(1036,674)(1036,674)
\qbezier(813,641)(918,649)(918,649)
\qbezier(692,639)(813,641)(813,641)
}
\textcolor{green}{
\qbezier(692,639)(6230,3269)(6230,3269)
}
\textcolor{blue}{
\qbezier(6200,653)(6230,639)(6230,639)
\qbezier(6170,667)(6200,653)(6200,653)
\qbezier(6140,681)(6170,667)(6170,667)
\qbezier(6110,695)(6140,681)(6140,681)
\qbezier(6054,718)(6110,695)(6110,695)
\qbezier(5998,738)(6054,718)(6054,718)
\qbezier(5939,756)(5998,738)(5998,738)
\qbezier(5881,769)(5939,756)(5939,756)
\qbezier(5853,773)(5881,769)(5881,769)
\qbezier(5826,776)(5853,773)(5853,773)
\qbezier(5812,777)(5826,776)(5826,776)
\qbezier(5799,778)(5812,777)(5812,777)
\qbezier(5785,778)(5799,778)(5799,778)
\qbezier(5771,779)(5785,778)(5785,778)
\qbezier(5756,778)(5771,779)(5771,779)
\qbezier(5740,778)(5756,778)(5756,778)
\qbezier(5725,777)(5740,778)(5740,778)
\qbezier(5710,776)(5725,777)(5725,777)
\qbezier(5679,772)(5710,776)(5710,776)
\qbezier(5648,767)(5679,772)(5679,772)
\qbezier(5595,755)(5648,767)(5648,767)
\qbezier(5541,739)(5595,755)(5595,755)
\qbezier(5483,718)(5541,739)(5541,739)
\qbezier(5425,693)(5483,718)(5483,718)
\qbezier(5366,667)(5425,693)(5425,693)
\qbezier(5307,639)(5366,667)(5366,667)
\qbezier(5250,612)(5307,639)(5307,639)
\qbezier(5193,586)(5250,612)(5250,612)
\qbezier(5133,561)(5193,586)(5193,586)
\qbezier(5073,539)(5133,561)(5133,561)
\qbezier(5016,522)(5073,539)(5073,539)
\qbezier(4959,510)(5016,522)(5016,522)
\qbezier(4930,505)(4959,510)(4959,510)
\qbezier(4901,502)(4930,505)(4930,505)
\qbezier(4887,501)(4901,502)(4901,502)
\qbezier(4872,500)(4887,501)(4887,501)
\qbezier(4857,500)(4872,500)(4872,500)
\qbezier(4843,500)(4857,500)(4857,500)
\qbezier(4829,500)(4843,500)(4843,500)
\qbezier(4815,500)(4829,500)(4829,500)
\qbezier(4801,501)(4815,500)(4815,500)
\qbezier(4787,502)(4801,501)(4801,501)
\qbezier(4759,505)(4787,502)(4787,502)
\qbezier(4731,510)(4759,505)(4759,505)
\qbezier(4672,523)(4731,510)(4731,510)
\qbezier(4613,541)(4672,523)(4672,523)
\qbezier(4559,561)(4613,541)(4613,541)
\qbezier(4505,583)(4559,561)(4559,561)
\qbezier(4475,597)(4505,583)(4505,583)
\qbezier(4445,610)(4475,597)(4475,597)
\qbezier(4415,624)(4445,610)(4445,610)
\qbezier(4385,639)(4415,624)(4415,624)
\qbezier(4329,665)(4385,639)(4385,639)
\qbezier(4273,691)(4329,665)(4329,665)
\qbezier(4211,717)(4273,691)(4273,691)
\qbezier(4148,739)(4211,717)(4211,717)
\qbezier(4092,756)(4148,739)(4148,739)
\qbezier(4036,768)(4092,756)(4092,756)
\qbezier(4007,773)(4036,768)(4036,768)
\qbezier(3978,776)(4007,773)(4007,773)
\qbezier(3964,777)(3978,776)(3978,776)
\qbezier(3949,778)(3964,777)(3964,777)
\qbezier(3935,778)(3949,778)(3949,778)
\qbezier(3920,779)(3935,778)(3935,778)
\qbezier(3905,778)(3920,779)(3920,779)
\qbezier(3890,778)(3905,778)(3905,778)
\qbezier(3876,777)(3890,778)(3890,778)
\qbezier(3861,775)(3876,777)(3876,777)
\qbezier(3831,772)(3861,775)(3861,775)
\qbezier(3801,767)(3831,772)(3831,772)
\qbezier(3744,754)(3801,767)(3801,767)
\qbezier(3687,736)(3744,754)(3744,754)
\qbezier(3634,716)(3687,736)(3687,736)
\qbezier(3580,694)(3634,716)(3634,716)
\qbezier(3550,681)(3580,694)(3580,694)
\qbezier(3519,667)(3550,681)(3550,681)
\qbezier(3489,652)(3519,667)(3519,667)
\qbezier(3458,638)(3489,652)(3489,652)
\qbezier(3399,610)(3458,638)(3458,638)
\qbezier(3341,583)(3399,610)(3399,610)
\qbezier(3286,561)(3341,583)(3341,583)
\qbezier(3232,541)(3286,561)(3286,561)
\qbezier(3172,523)(3232,541)(3232,541)
\qbezier(3113,510)(3172,523)(3172,523)
\qbezier(3085,505)(3113,510)(3113,510)
\qbezier(3056,502)(3085,505)(3085,505)
\qbezier(3042,501)(3056,502)(3056,502)
\qbezier(3028,500)(3042,501)(3042,501)
\qbezier(3014,500)(3028,500)(3028,500)
\qbezier(2999,500)(3014,500)(3014,500)
\qbezier(2984,500)(2999,500)(2999,500)
\qbezier(2969,500)(2984,500)(2984,500)
\qbezier(2955,501)(2969,500)(2969,500)
\qbezier(2940,502)(2955,501)(2955,501)
\qbezier(2910,506)(2940,502)(2940,502)
\qbezier(2880,511)(2910,506)(2910,506)
\qbezier(2825,523)(2880,511)(2880,511)
\qbezier(2771,540)(2825,523)(2825,523)
\qbezier(2709,562)(2771,540)(2771,540)
\qbezier(2648,588)(2709,562)(2709,562)
\qbezier(2595,612)(2648,588)(2648,588)
\qbezier(2542,637)(2595,612)(2595,612)
\qbezier(2511,652)(2542,637)(2542,637)
\qbezier(2480,666)(2511,652)(2511,652)
\qbezier(2449,681)(2480,666)(2480,666)
\qbezier(2417,695)(2449,681)(2449,681)
\qbezier(2365,717)(2417,695)(2417,695)
\qbezier(2312,736)(2365,717)(2365,717)
\qbezier(2255,754)(2312,736)(2312,736)
\qbezier(2197,767)(2255,754)(2255,754)
\qbezier(2167,772)(2197,767)(2197,767)
\qbezier(2137,776)(2167,772)(2167,772)
\qbezier(2122,777)(2137,776)(2137,776)
\qbezier(2107,778)(2122,777)(2122,777)
\qbezier(2092,778)(2107,778)(2107,778)
\qbezier(2077,779)(2092,778)(2092,778)
\qbezier(2062,778)(2077,779)(2077,779)
\qbezier(2047,778)(2062,778)(2062,778)
\qbezier(2032,777)(2047,778)(2047,778)
\qbezier(2017,776)(2032,777)(2032,777)
\qbezier(1987,772)(2017,776)(2017,776)
\qbezier(1957,767)(1987,772)(1987,772)
\qbezier(1904,755)(1957,767)(1957,767)
\qbezier(1851,740)(1904,755)(1904,755)
\qbezier(1791,718)(1851,740)(1851,740)
\qbezier(1731,693)(1791,718)(1791,718)
\qbezier(1672,666)(1731,693)(1731,693)
\qbezier(1614,639)(1672,666)(1672,666)
\qbezier(1555,611)(1614,639)(1614,639)
\qbezier(1496,584)(1555,611)(1555,611)
\qbezier(1439,561)(1496,584)(1496,584)
\qbezier(1383,540)(1439,561)(1439,561)
\qbezier(1328,523)(1383,540)(1383,540)
\qbezier(1273,511)(1328,523)(1328,523)
\qbezier(1243,506)(1273,511)(1273,511)
\qbezier(1214,502)(1243,506)(1243,506)
\qbezier(1199,501)(1214,502)(1214,502)
\qbezier(1184,500)(1199,501)(1199,501)
\qbezier(1169,500)(1184,500)(1184,500)
\qbezier(1155,500)(1169,500)(1169,500)
\qbezier(1140,500)(1155,500)(1155,500)
\qbezier(1125,500)(1140,500)(1140,500)
\qbezier(1110,501)(1125,500)(1125,500)
\qbezier(1095,502)(1110,501)(1110,501)
\qbezier(1065,506)(1095,502)(1095,502)
\qbezier(1036,511)(1065,506)(1065,506)
\qbezier(977,524)(1036,511)(1036,511)
\qbezier(918,542)(977,524)(977,524)
\qbezier(865,561)(918,542)(918,542)
\qbezier(813,583)(865,561)(865,561)
\qbezier(782,597)(813,583)(813,583)
\qbezier(752,611)(782,597)(782,597)
\qbezier(722,625)(752,611)(752,611)
\qbezier(692,639)(722,625)(722,625)
}
\qbezier(692,500)(692,4500)(692,4500)
\qbezier(648,639)(692,639)(692,639)
\qbezier(670,825)(692,825)(692,825)

\qbezier(670,1011)(692,1011)(692,1011)
\qbezier(670,1197)(692,1197)(692,1197)
\qbezier(670,1383)(692,1383)(692,1383)
\qbezier(648,1569)(692,1569)(692,1569)
\qbezier(670,1755)(692,1755)(692,1755)
\qbezier(670,1941)(692,1941)(692,1941)
\qbezier(670,2127)(692,2127)(692,2127)
\qbezier(670,2313)(692,2313)(692,2313)
\qbezier(648,2500)(692,2500)(692,2500)
\qbezier(670,2686)(692,2686)(692,2686)
\qbezier(670,2872)(692,2872)(692,2872)
\qbezier(670,3058)(692,3058)(692,3058)
\qbezier(670,3244)(692,3244)(692,3244)
\qbezier(648,3430)(692,3430)(692,3430)
\qbezier(670,3616)(692,3616)(692,3616)
\qbezier(670,3802)(692,3802)(692,3802)
\qbezier(670,3988)(692,3988)(692,3988)
\qbezier(670,4174)(692,4174)(692,4174)
\qbezier(648,4360)(692,4360)(692,4360)
\qbezier(692,639)(6230,639)(6230,639)
\qbezier(927,623)(927,639)(927,639)

\qbezier(1162,623)(1162,639)(1162,639)
\qbezier(1397,623)(1397,639)(1397,639)
\qbezier(1632,623)(1632,639)(1632,639)
\qbezier(1867,606)(1867,639)(1867,639)
\qbezier(2102,623)(2102,639)(2102,639)
\qbezier(2337,623)(2337,639)(2337,639)
\qbezier(2572,623)(2572,639)(2572,639)
\qbezier(2807,623)(2807,639)(2807,639)
\qbezier(3042,606)(3042,639)(3042,639)
\qbezier(3277,623)(3277,639)(3277,639)
\qbezier(3512,623)(3512,639)(3512,639)
\qbezier(3748,623)(3748,639)(3748,639)
\qbezier(3983,623)(3983,639)(3983,639)
\qbezier(4218,606)(4218,639)(4218,639)
\qbezier(4453,623)(4453,639)(4453,639)
\qbezier(4688,623)(4688,639)(4688,639)
\qbezier(4923,623)(4923,639)(4923,639)
\qbezier(5158,623)(5158,639)(5158,639)
\qbezier(5393,606)(5393,639)(5393,639)
\qbezier(5628,623)(5628,639)(5628,639)
\qbezier(5863,623)(5863,639)(5863,639)
\qbezier(6098,623)(6098,639)(6098,639)
\end{picture}
\[ [/tex]

Note that A has zero velocity when it makes contact with ground.
Of course, A is just representative of one point on the wheel.
Each point has it own set of curves, slightly displaced in time from A.

For this to happen, [tex] v_G=\omega R [/tex].
 
Last edited:
  • #3
So if there is relative motion between two surfaces in contact then there must be a friction force?
 
  • #4
Benny said:
So if there is relative motion between two surfaces in contact then there must be a friction force?
Yes...but its magnitude is proportional to the coefficent of kinetic/sliding-friction.
 
  • #5
Benny said:
Hi, I don't understand the difference between rolling with and without slipping. To put my question into some kind of context, consider a ball of radius r which rolls to the right along the x (horizontal) axis. The ball is traveling at a constant velocity v and continues rolling until it reaches a curved hill, eventually stopping at some distance H above the x-axis. If there is no friction between the x-axis and the ball then H can be found by solving (1/2)mv^2 + (1/2)Iw^2 = mgH...(1).
Just to be clear: There is certainly friction between the ball and the ground, but it will be static friction. (As robphy explains, there will be no sliding/kinetic friction.) If the surfaces were frictionless, then the ball's rotational speed would not change as it went uphill.

Just to be clearer: As the ball rolls without slipping on the horizontal surface, the static friction force is zero. But as it rolls uphill, there will be a non-zero static friction force on the ball.
 
  • #6
Just to add one thing that hasn't been explicitly mentioned...
since there is no relative motion at the point of contact when "rolling without slipping", no work is being done by the frictional forces.
 
  • #7
Thanks for the help guys.
 

1. What is the difference between rolling with and without slipping?

Rolling with and without slipping refer to two different types of motion for a rolling object. Rolling without slipping means that the object is rolling smoothly without any sliding or slipping of the contact point with the surface. Rolling with slipping, on the other hand, refers to a situation where there is some sliding or slipping of the contact point with the surface.

2. How is rolling with and without slipping affected by friction?

In both cases, friction plays an important role. In the case of rolling without slipping, the friction force between the object and the surface helps to maintain the rolling motion without any slipping. In the case of rolling with slipping, the friction force can either help or hinder the rolling motion, depending on the direction and magnitude of the force.

3. What factors affect the ability of an object to roll without slipping?

The ability of an object to roll without slipping is affected by several factors, including the shape and size of the object, the surface it is rolling on, and the force applied to it. A larger object with a larger surface area and a rougher surface will have a better ability to roll without slipping compared to a smaller object with a smooth surface.

4. How do you calculate the velocity of an object rolling without slipping?

The velocity of an object rolling without slipping can be calculated using the formula v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius of the rolling object. This formula holds true as long as the object is rolling without slipping and there is no external force acting on it.

5. Can an object roll without slipping on an inclined plane?

Yes, an object can roll without slipping on an inclined plane as long as the force of gravity acting on the object is balanced by the normal force from the inclined plane, and the friction force is enough to prevent slipping. The angle of the incline, as well as the mass and shape of the object, will affect the ability to roll without slipping on an inclined plane.

Similar threads

Question regarding Rolling with and without Slipping and Sliding
    • Introductory Physics Homework Help
Replies
4
Views
1K
Kinetic Energy of a Cylinder Rolling Without Slipping
    • Introductory Physics Homework Help
Replies
21
Views
1K
A cylinder of snow rolls down a hill gathering more snow -- calculate its speed
    • Introductory Physics Homework Help
2
Replies
39
Views
2K
Acceleration of system related to rolling motion and pulley
    • Introductory Physics Homework Help
2
Replies
35
Views
2K
Wooden sphere rolling on a double metal track
    • Introductory Physics Homework Help
3
Replies
97
Views
3K
Coin Slipping on a Spinning Wheel
    • Introductory Physics Homework Help
Replies
20
Views
1K
Mechanics: A bowling ball is thrown and rolls with slipping
    • Introductory Physics Homework Help
Replies
8
Views
2K
Forces when car wheels "lay rubber"
    • Introductory Physics Homework Help
Replies
5
Views
865
Horizontal impulse on a ball at rest on a plane (with friction)
    • Introductory Physics Homework Help
Replies
14
Views
1K
Cylinder Rolling Down an Incline Without Slipping
    • Introductory Physics Homework Help
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top