A car holds a steady 10 m/s around a flat circular curve of radius 20 m.
What is its centripetal acceleration?
Start with the car's own numbers: v = 10 m/s, r = 20 m.
Square the speed, and divide by the radius: (10 × 10) / 20 = 5. The car's centripetal acceleration is 5 m/s².
That move is the equation you have seen: a = v²/r.
Step 1: write down the values in the question, and mark the unknown.
Step 2: write down the equation.
Step 3: substitute in the values, and calculate. The result line always carries its unit: m/s².
Every case here is steady-speed circular motion: v is the steady speed, and r is the circle's radius.
A car holds a steady 10 m/s around a flat circular curve of radius 20 m. Calculate its centripetal acceleration.
Write down the values:
v = 10 m/s, r = 20 m, a = ?
Write down the equation:
a = v²/r
Substitute in the values, and calculate:
a = (10 × 10) / 20 = 5
The car's centripetal acceleration is 5 m/s².
A passenger train takes a wide circular curve of radius 300 m at a steady 30 m/s. Calculate its centripetal acceleration.
Write down the values:
v = 30 m/s, r = 300 m, a = ?
Write down the equation:
a = v²/r
Substitute in the values, and calculate:
a = (30 × 30) / 300 = 3
The train's centripetal acceleration is 3 m/s².
A remote-control car circles a flat loop of radius 4 m at a steady 6 m/s. Enter its centripetal acceleration in m/s².
A car rounds a flat traffic circle of radius 30 m at a steady 12 m/s. Enter its centripetal acceleration in m/s².
A go-kart holds a steady 16 m/s around a flat circular corner of radius 32 m. Enter its centripetal acceleration in m/s².
A motorcycle rounds a flat circular bend of radius 50 m at a steady 15 m/s. Enter its centripetal acceleration in m/s².
A sports car laps a flat circular test pad of radius 45 m at a steady 18 m/s. Enter its centripetal acceleration in m/s².
A track cyclist holds a steady 14 m/s around a flat circular course of radius 28 m. Enter her centripetal acceleration in m/s².
A horse gallops a circular training ring of radius 22 m at a steady 11 m/s. Enter its centripetal acceleration in m/s².
A bus takes a flat circular highway ramp of radius 65 m at a steady 13 m/s. Enter its centripetal acceleration in m/s².
A car joins a long, flat highway curve that forms part of a circle of radius 160 m. Its cruise control holds a steady 24 m/s the whole way around the curve. Enter its centripetal acceleration in m/s².