# Centripetal acceleration formula

• BensonCa
In summary, the riders on the carnival ride experience a centripetal acceleration of 26 m/s^2 due to the circular motion of the room with a radius of 9.1m and an angular speed of 1.7 rad/s. This can be calculated using the formula a = w^2 r, where w is the angular speed and r is the radius. Alternatively, it can also be calculated using the formula a = v^2/r, where v is the linear speed and r is the radius.
BensonCa

## Homework Statement

In a certain carnival ride, visitors enter a circular room with radius r=9.1m. The room then begins spinning around its center, reaching an angular speed of 1.7rad/s. What centripetal acceleration do the riders experience?

ac= v^2/r

## The Attempt at a Solution

I believed that ac= v^2/r which would equal .3175824176 or .32 m/s^2

but the answer is 26 m/s^2 and the explanation is Centripetal acceleration is given by ac=rω2. WHY?

You're given angular speed, and you're trying to plug it into a formula with velocity.

BensonCa
Good effort though! You have omega, the formula you want to be using is a = w^2 r substituting w = v/r into the original formula you have.

BensonCa
Oh, I see what I did, thank you

I would rather go with:
v= wr
v =1.7 x 9.1 = 15.47

to find the acceleration:
a = v^2/r
a = (15.47)^2/9.1
a = 231.32/9.1
a = 26.299 ( and can be rounded to 26)

## 1. What is the formula for centripetal acceleration?

The formula for centripetal acceleration is a = v²/r, where a is the acceleration, v is the velocity, and r is the radius of the circular motion.

## 2. How is centripetal acceleration different from regular acceleration?

Centripetal acceleration is a type of acceleration that occurs when an object moves in a circular path. Unlike regular acceleration, which is a change in an object's speed or direction, centripetal acceleration is a change in the direction of an object's velocity towards the center of the circle.

## 3. What is the unit of measurement for centripetal acceleration?

The unit of measurement for centripetal acceleration is meters per second squared (m/s²).

## 4. Can the centripetal acceleration formula be used for any circular motion?

Yes, the centripetal acceleration formula can be used for any circular motion, as long as the acceleration is constant and the object is moving at a constant speed.

## 5. How does centripetal acceleration relate to centripetal force?

Centripetal acceleration and centripetal force are closely related. Centripetal acceleration is the acceleration required to keep an object moving in a circular path, while centripetal force is the force that causes this acceleration. The centripetal force is directed towards the center of the circle and is equal to the product of the mass and centripetal acceleration.

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