A rider circles on a merry-go-round at a steady 5 m/s. Lap after lap, the ride feels the same. Some quantities of her motion really are constant. Others never stop changing.
Which quantities stay constant, and which change continuously?
Sort each quantity with one question: does it read the same at every point of the circle?
Her speed is constant. It reads 5 m/s at every point.
Her distance from the center is constant, because the circle's radius does not change. The time each lap takes is constant too.
Her direction of travel changes continuously. At every point she is headed a new way.
Velocity includes direction. So her velocity changes continuously, even though her speed does not.
Her acceleration always points toward the center. But the center sits in a new direction as she moves around the circle, so the direction of her acceleration changes continuously too.
The sort reads the acceleration's direction only. The acceleration's size waits for a later lesson.
A bus circles a traffic circle at a steady 7 m/s. Is its speed constant or continuously changing?
A horse on a carousel moves at a steady pace. Is its direction of travel constant or continuously changing?
A model train runs a circular track at a steady 3 m/s. Is its velocity constant or continuously changing?
A go-kart laps a circular track at a steady 8 m/s. Sort these two quantities: the go-kart's speed, and the go-kart's velocity.
The speed reads 8 m/s at every point of the lap, so the speed is constant.
The go-kart's direction of travel is new at every point, and velocity includes direction, so the velocity changes continuously.
The speed is constant; the velocity changes continuously.
A cyclist rides a flat circular track at a steady 9 m/s. Which quantity stays constant for the whole ride?
A scooter circles a fountain at a steady 5 m/s. Which quantity continuously changes?
A ball on a string circles a post at a constant speed. Which quantity reads the same at every point of the circle?