# Finding centripedal acceleration with tangential acceleration

• tobtob
In summary, the conversation discusses finding the centripetal acceleration of a roller coaster at a specific point in time using experimental data of acceleration in the X, Y, and Z directions. It is suggested to integrate the acceleration to find the velocity, assuming the initial velocity is zero. This can then be used to determine the direction of the curvature and ultimately the centripetal acceleration at the desired point. It is noted that this task is challenging due to error accumulation.
tobtob

## Homework Statement

I'm trying to find the centripedal acceleration of a roller coaster at a certain point in time from experimental data of acceleration in the X, Y, and Z directions. I do not know the velocity of the roller coaster, only the acceleration. Thank you!

v^2/r

## The Attempt at a Solution

Could I possibly integrate something to find velocity?

If you integrate the acceleration you'll get velocity, assuming you know the initial velocity - which should be zero for a roller-coaster.

Integrating again will give you position, so you now have an empirical function that describes the curve that is the roller-coaster track.

Using that, you can apply the techniques described in this to work out the direction of the curvature at any point on the track, and by combining that with your accel measurements, obtain the centripetal acceleration at that point.

tobtob
This sounds like an exercise in inertial navigation. This is notoriously difficult because of the rate of error accumulation. You will need extremely detailed data from a known resting start.

## What is centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle.

## What is tangential acceleration?

Tangential acceleration is the acceleration experienced by an object moving in a circular path that is tangent to the circle. It is always perpendicular to the centripetal acceleration.

## How are centripetal and tangential acceleration related?

Centripetal and tangential acceleration are related by the formula ac = v2/r, where ac is the centripetal acceleration, v is the tangential velocity, and r is the radius of the circular path.

## How do you find centripetal acceleration with tangential acceleration?

To find centripetal acceleration with tangential acceleration, you can use the formula ac = at/r, where ac is the centripetal acceleration, at is the tangential acceleration, and r is the radius of the circular path.

## What are some examples of objects experiencing centripetal acceleration with tangential acceleration?

Some examples include a car going around a curve, a satellite orbiting Earth, and a person on a swing.

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