Centripetal Force

Anything moving in a circle is constantly changing direction, and that change requires a force pointed toward the center of the circle. Without this inward pull, the object would fly off in a straight line instead of curving.

a = v² / r

• a — centripetal acceleration (m/s²): how quickly the object's direction changes toward the center
• v — speed (m/s): how fast the object moves along the circular path
• r — radius (m): the distance from the object to the center of the circle

An object moves in a circle of radius 2 meters at a speed of 4 meters per second. What is its centripetal acceleration?

• v = 4 m/s
• r = 2 m

1. a = v² / r
2. a = (4 m/s)² / 2 m

a = 8 m/s²

The same object now circles at 8 meters per second, still at a 2 meter radius. What is its centripetal acceleration?

• 16 m/s²
• 8 m/s²
• 32 m/s²

Keep the speed at 4 meters per second, but double the radius to 4 meters. What happens to the acceleration?

• 4 m/s²
• 16 m/s²
• 8 m/s²