Elif's carousel gets a motor adjustment. A full turn used to take 10 s. Now a full turn takes 5.0 s. Her seat keeps the same circle.
What happens to Elif's speed?
Elif's circle has not changed, so the distance she covers in one turn has not changed: one circumference, 2πr.
Her period has changed. The same trip now takes half the time.
Speed is distance traveled divided by the time taken.
The same distance in half the time is twice the speed. Elif now moves twice as fast.
The trade is exact. Halve the period and the speed doubles. Double the period and the speed halves.
Watch what stays fixed: the distance per turn. Only the time for that distance changes.
Fergus cranks a salad spinner harder, and the basket's period drops from 0.8 s to 0.4 s. The basket keeps its size. What happens to the speed of a lettuce leaf at the rim?
A box fan is switched to a faster setting. Each blade turn takes less time, and a point on a blade moves faster. Why is the point faster?
A potter's wheel is switched to a slower setting, so each turn takes twice the time. A clay fleck on the rim keeps its circle. What happens to the fleck's speed?
The fleck's circle is unchanged, so its distance per turn is unchanged.
Each turn now takes twice the time.
The same distance in twice the time is half the speed.
The fleck's speed halves.
A ceiling fan is switched from low to high, and each turn now takes one third of the time. What happens to the speed of a point on a blade?
The point's circle is unchanged, so its distance per turn is unchanged.
Each turn now takes one third of the time.
The same distance in one third of the time is three times the speed.
The point moves three times as fast.
A display turntable is set so that each turn takes three times as long as before. The platter keeps its size. What happens to the speed of a point on its edge?
A Ferris wheel runs a slow maintenance cycle: each revolution takes 80 s instead of the usual 40 s. The wheel keeps its size. What happens to a cabin's speed?
A record player is switched from 45 turns per minute to a slower setting, and the speed of a point on the record's edge halves. The record keeps its size. Which change caused that?
Golda's drone flies a circular loop at a steady 3.0 m/s, one lap every 8.0 s. She retunes it so a lap takes 4.0 s on the same circle. Enter the drone's new speed in m/s, to the nearest 0.1 m/s. Answers within 0.1 m/s are accepted.