A car leaves the highway on a tight circular ramp of radius 25 m, holding a steady 12 m/s. The next exit uses a gentle circular ramp of radius 75 m, and the car takes that one at the same steady 12 m/s. Same car, same speed, one thing changed: the radius.
On which ramp is the car's centripetal acceleration greater?
You have seen how the speed changes the centripetal acceleration at a fixed radius. Now hold the speed fixed and change the radius.
A smaller radius is a tighter curve: the direction of travel has to swing around in less room.
Hold the speed fixed and widen the radius: the centripetal acceleration gets smaller.
So on the tight 25 m ramp, the car's centripetal acceleration is greater than on the gentle 75 m ramp.
A later lesson gives the exact relationship. Here, the direction of the change is the point.
A motorcycle rounds a tight circular curve of radius 18 m, then a gentle one of radius 54 m, at the same steady speed. Compare its centripetal acceleration on the tight curve.
A dog runs a small circular loop, then a loop twice as wide, at the same steady pace. Compare its centripetal acceleration on the wider loop.
A skater glides at a steady 4 m/s around a circle of radius 5 m, then around a circle of radius 10 m at the same speed. Compare her centripetal accelerations.
The speed is the same on both circles. Only the radius differs.
A tighter circle at the same speed means a greater centripetal acceleration.
Her centripetal acceleration is greater on the 5 m circle.
Jasper says: at the same steady speed, a bus has a smaller centripetal acceleration on a wide traffic circle than on a tight one. Is he correct?
A pickup drives a curve of radius 30 m and later a curve of radius 90 m, at the same steady speed. Which statement is correct?
The same sports car laps four flat circular test tracks at the same steady speed. The tracks' radii are 10 m, 25 m, 40 m, and 80 m. On which track is the car's centripetal acceleration greatest?
A subway train and a freight train move at the same steady speed, each on its own circular section of track. The subway train's centripetal acceleration is smaller. Which statement follows?