A go-kart holds a steady 8 m/s around a flat circular loop of radius 16 m. You have seen that a greater speed on the same circle means a greater centripetal acceleration, and that a tighter circle at the same speed does too.
How large is the go-kart's centripetal acceleration?
Work the go-kart from its numbers first. Square the speed, and divide by the radius: (8 × 8) / 16 = 4.
That number, 4 m/s², is the go-kart's centripetal acceleration. Could you do the same for any circle?
Well, there is an equation for exactly this move.
a: centripetal acceleration (m/s²) · v: speed (m/s) · r: radius (m).
The units work out: (m/s)² is m²/s², and m²/s² divided by m is m/s².
The speed is squared. That is why doubling the speed at a fixed radius makes the centripetal acceleration four times as large.
The worked examples below run the routine in full, then double the speed to watch the square bite.
A go-kart holds a steady 8 m/s around a flat circular loop of radius 16 m. Calculate its centripetal acceleration.
Write down the values:
v = 8 m/s, r = 16 m, a = ?
Write down the equation:
a = v²/r
Substitute in the values, and calculate:
a = (8 × 8) / 16 = 4
The go-kart's centripetal acceleration is 4 m/s².
The same go-kart doubles its speed to a steady 16 m/s on the same 16 m loop. Calculate its centripetal acceleration now.
Write down the values:
v = 16 m/s, r = 16 m, a = ?
Write down the equation:
a = v²/r
Substitute in the values, and calculate:
a = (16 × 16) / 16 = 16
Now a = 16 m/s². Doubling the speed made the centripetal acceleration four times as large.
A van rounds a flat circular curve of radius 5 m at a steady 6 m/s. Enter its centripetal acceleration in m/s².
A cart's steady speed on a fixed circle doubles. By a = v²/r, what happens to its centripetal acceleration?
Kaia says: with the speed in m/s and the radius in m, v²/r comes out in m/s², which is an acceleration unit. Is she correct?
A race car holds a steady 12 m/s around a flat circular test pad of radius 16 m. Enter its centripetal acceleration in m/s².
Which equation gives the centripetal acceleration of an object in steady-speed circular motion?
A cyclist's centripetal acceleration on a flat circular loop is 2.5 m/s² at a steady 6 m/s. She doubles her speed to a steady 12 m/s on the same loop. Enter her new centripetal acceleration in m/s².