Describing Motion Around Us
Going round in circles
See why moving in a circle at steady speed is still accelerating.
Not only straight lines. So far, things moved along a line. Motion can also happen:
- in a plane (two directions): overtaking a car, a kicked football, a satellite;
- in space (three directions): a car on a winding mountain road, a flying bird.
On a merry-go-round. A child goes from A, past B, to C, halfway round.
- Distance = the curved path ABC.
- Displacement = the straight line from A to C.
After one full round: distance = the whole circle, 2πR (R is the radius); displacement = 0, because the child is back at the start.
Speed round a circle. If one round takes time T, the average speed is v_av = 2πR ÷ T: one circle's length divided by the time. The average velocity over a full round is 0.
Uniform circular motion means going round a circle at a constant speed. The speedometer reading does not change.
But it is still accelerating! Picture an athlete on tracks with more and more sides. On a rectangle she turns 4 times a lap; on a hexagon, 6 times. With more and more sides, the track becomes a circle, and she is turning all the time. Her direction keeps changing, so her velocity keeps changing, even though her speed doesn't. A changing velocity is acceleration.
Which way does it want to go? At every point, the velocity points along the tangent: a line that just touches the circle at that point. Try the book's activity: roll a marble round inside a ring, then lift the ring. The marble shoots off in a straight line along the tangent. A car on an icy bend slides straight on for the same reason: to go round, something must keep turning it.
Why it matters. Uniform circular motion is an ideal model, but a useful one: for planets going round the Sun and vehicles taking circular turns.
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