How to play Carousel
- Choose a ride and read the radius, speed, period, or angular velocity on its card.
- Use T = 2πr ÷ v, ω = 2π ÷ T, v = ω·r, or θ = ω·t to find the answer.
- Type your answer and press Start. A time stops the ride, an angular velocity spins it, a speed flies the drone, and an angle plants your flag.
- Watch the θ–t graph: a steady turn draws a straight line, and its slope is the angular velocity ω.
What is uniform circular motion?
An object in uniform circular motion goes around a circle at constant speed. It covers equal angles in equal times, so its angle grows steadily: θ = ω·t, where ω is the angular velocity in radians per second. One lap is 2π rad and takes the period T = 2π ÷ ω. A point at radius r travels the arc s = r·θ, so its speed is v = ω·r. Everything on a turning carousel has the same ω, but an outer horse moves faster than an inner one. The speed never changes, yet the velocity does, because its direction keeps turning along the circle.
A focused learning model
The carousel turns at one steady angular velocity with no speeding up or slowing down; the ride starts and stops instantly. The horse is a point at a fixed radius. Laps and the stop are found exactly. Every ride uses the same view and plays twice as fast as real time; long rides play faster, as shown on the canvas.