Question

what relationship exists between the radius of a circle and the centripetal acceleration​

Answer 1

The magnitude of the centripetal acceleration is directly proportional to the square of the speed and inversely proportional to the radius of the circle in which the object is traveling.

Answer 2

$a_{c} =\frac{v^{2} }{r}$, Centripetal acceleration is inversely proportional to radius of the circle.

Explanation:

• Uniform circular motion is a specific type of motion in which an object travels in a circle with a constant speed.
• The centripetal acceleration is the motion inwards towards the center of a circle.
• The acceleration is equal to the square of the velocity, divided by the radius of the circular path.
• In uniform circular motion, the direction of the velocity changes constantly, so there is always an associated acceleration, even though the magnitude of the velocity might be constant.

• Centripetal acceleration $a_{c}$ is the acceleration experienced while in uniform circular motion.
• It always points toward the center of rotation. It is perpendicular to the linear velocity v.

• Centripetal acceleration is inversely proportional to radius of the circle which is why the centripetal acceleration is greater for small radius circular motion.
• $a_{c} =\frac{v^{2} }{r}$