Running counter-clockwise
Drag to orbit
Blue ω sets the axis, green r points to the moving object, and orange v is tangent to the path.
Motion vector laboratory
Vectors &Rotation
Follow a point around a circle and discover why its velocity always points along the tangent—not toward the centre.
1Predict2Rotate3Connect
Change the motion
Watch both the direction and length of the velocity arrow.
Angular speed ωHow quickly the angle changes
Orbit radius rDistance from the rotation axis
Rotation directionThis reverses both ω and v
Show right-hand ruleIndex ω, middle r, thumb v
Linear speed0.25 m/s
Period6.28 s
Quick predictionIf r grows while ω stays fixed, what happens to speed?
Make a predictionThen move the radius slider and watch the orange arrow.
Three directions
ω follows the rotation axis, r points outward, and v follows the tangent.
Cross product
The right-hand rule determines the direction of the vector product.
v = ω × r
Speed grows two ways
A point moves faster if the object spins faster or if the point lies farther from the axis.
|v| = ωr
Try it
Discuss with AI →Double ω, then halve r. What happens to v?
Use the two sliders to test whether the effects cancel.