Rolling Without Slipping Calculator
Relate a wheel’s linear speed to its spin using v = ωr, and see the speed of the top, center and contact point.
How it works
v = ω·r · ω = v ÷ r · top-of-wheel speed = 2v · contact-point speed = 0 · distance per revolution = 2πr
Rolling without slipping means the contact patch does not skid, which locks the forward speed of the center to the spin by v = ωr. In this pure rolling state the point touching the ground is instantaneously at rest, the center moves at v, and the top of the wheel moves at 2v — the wheel effectively pivots about the contact point each instant. Break this condition, as on ice or under hard braking, and v no longer equals ωr because the tyre slides.
Worked example
A wheel of radius 0.35 m rolling at 10 m/s spins at ω = 10 ÷ 0.35 ≈ 28.57 rad/s, or about 273 rpm. It advances one circumference — 2π × 0.35 ≈ 2.20 m — per turn, its top races along at 20 m/s, and its contact point is momentarily motionless.
Sources: Rolling — Wikipedia
Frequently asked questions
Why is the contact point momentarily at rest?
In pure rolling the wheel’s spin carries the bottom point backward at exactly the speed the center moves forward, so the two cancel. The contact point has zero velocity for an instant, which is why rolling friction is so much smaller than sliding friction.
Why does the top of the wheel move at twice the center’s speed?
The top combines the center’s forward speed v with the rotational speed ωr = v pointing the same way, giving 2v. The bottom combines them in opposite directions, giving zero.
When does v = ωr stop holding?
Only while the wheel rolls without slipping. If it skids — spinning tyres on ice or a locked wheel braking — the surface slides under the wheel and the simple v = ωr relationship no longer applies.
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This calculator is for educational purposes. Double-check important results before acting on them.