# Tangental acceleration from given centripetal acceleration and a range of radii

• sneurlax
In summary, the conversation discusses how to determine the tangental acceleration needed to produce a given centripetal acceleration from a range of radii. The formula Vt^2=r*a_c is provided as a means to calculate the tangential speed, and an example is given using an asteroid with a 137km circumference. The conversation also mentions the possibility of using this concept to create artificial gravity.
sneurlax
Hi, how can I determine the tangental acceleration of a circle needed to produce a given centripetal acceleration from a range of radii? For example, I would like to produce 9.81 m/s/s centripetal acceleration with a range of radii from 5km to 100km? All I really need is to figure out the equation and I can write a program to graphically display the results.

Here's what I've found so far:

ac = vt2/r
centripetal acceleration = (tangental acceleration)2 / radius of circular path

Fc = mvt2/r
centripetal force = mass x ((tangental speed)2 / radius of circular path)

If centripetal force is different than centripetal acceleration and a weight is needing to determine the Newtons involved then assume that the object being acted upon weighs 80 Earth kg.

Thanks for any help! If you could just nudge me in the right direction I'd appreciate it very much.

You don't need a tangential acceleration to produce a given centripetal acceleration, all you need is a given tangential speed. This can be calculated from the first formula you gave.

Vt^2=r*a_c
where r are the different radii and a_c is the centripetal acceleration.

... d'oh

That seems so obvious now.

Anyways, that means that an asteroid with a 137km circumference ring drilled into it (the longest manmade tunnel so far) would need to be accelerated to a spin 59.4km/h (instantaneous velocity tangental to the ring) to produce 9.81 m/s2 acceleration... artificial gravity, anyone?

## 1. What is tangential acceleration?

Tangential acceleration is the rate of change of tangential velocity. It is the component of acceleration that is parallel to the object's motion along a curved path.

## 2. How is tangential acceleration related to centripetal acceleration?

Tangential acceleration and centripetal acceleration are mathematically related through the formula a = v^2/r, where a is the centripetal acceleration, v is the tangential velocity, and r is the radius of the circular motion. Tangential acceleration is dependent on the object's speed and the radius of the circular path, while centripetal acceleration is dependent on the object's mass and the force acting towards the center of the circular path.

## 3. Can tangential acceleration be negative?

Yes, tangential acceleration can be negative if the object is slowing down while moving in a circular path. This occurs when the tangential velocity decreases, resulting in a negative rate of change and a negative tangential acceleration.

## 4. How does the radius of the circular path affect tangential acceleration?

The radius of the circular path has a direct impact on tangential acceleration. As the radius decreases, the object's tangential velocity increases, resulting in a higher tangential acceleration. Conversely, as the radius increases, the tangential velocity decreases, resulting in a lower tangential acceleration.

## 5. How can I calculate tangential acceleration from given centripetal acceleration and a range of radii?

To calculate tangential acceleration, you can use the formula a = v^2/r, where a is the tangential acceleration, v is the tangential velocity (which can be found using the formula v = ωr, where ω is the angular velocity), and r is the radius of the circular path. You can also use the formula a = √(a^2 - ac^2), where a is the total acceleration and ac is the centripetal acceleration. This method allows you to find the tangential acceleration without knowing the tangential velocity.

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