# Tangential & normal acceleration derivations

• Markel
In summary, tangential acceleration is the rate of change of an object's tangential velocity and is calculated using a<sub>t</sub> = v<sub>t</sub> / t. Normal acceleration, on the other hand, is the rate of change of an object's normal velocity and is calculated using a<sub>n</sub> = v<sub>n</sub> / t. These two accelerations are related by the formula a = √(a<sub>t</sub><sup>2</sup> + a<sub>n</sub><sup>2</sup>), and together they make up the total acceleration of an object. In real-world applications, tangential and normal acceleration are commonly used in

#### Markel

I'm trying to understand how my book derives the tangential accelration. I drew a picture because it's kind of confusing to explain.

From the triangle we get the tangential and normal components of the velocity.

What my problem is (and I think, and hope, it's something simple that I just can't see) that in the second equation where they find SQ.

They times they take adjacent x sin(angle) = oposite.

but isn't sin = oposite/hypoteneuse ??

shouldn't the formula be adjacent x tan(angle) = opposite = SQ ?

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oops. figured this out. Sorry, this was really silly.

## 1. What is tangential acceleration and how is it calculated?

Tangential acceleration is the rate of change of an object's tangential velocity. It is calculated using the formula at = vt / t, where at is tangential acceleration, vt is tangential velocity, and t is time.

## 2. How is normal acceleration different from tangential acceleration?

Normal acceleration is the rate of change of an object's normal velocity, which is the component of velocity perpendicular to the object's tangential velocity. It is calculated using the formula an = vn / t, where an is normal acceleration, vn is normal velocity, and t is time.

## 3. What is the relationship between tangential and normal acceleration?

Tangential and normal acceleration are perpendicular to each other and together they make up the total acceleration of an object. They are related by the formula a = √(at2 + an2), where a is total acceleration.

## 4. How are tangential and normal acceleration used in real-world applications?

Tangential and normal acceleration are commonly used in physics and engineering to study the motion of objects. They are particularly useful in understanding circular motion, such as the motion of planets around the sun or the motion of cars around a curved track. They are also important in designing and analyzing rotational systems, such as wheels and gears.

## 5. What are some common misconceptions about tangential and normal acceleration?

One common misconception is that tangential and normal acceleration are the same as centripetal and centrifugal acceleration, respectively. While they are related, they are not the same and have different formulas and meanings. Another misconception is that tangential acceleration is always in the direction of motion, but this is only true if the object is moving in a straight line. In circular motion, tangential acceleration can be in any direction, depending on the object's speed and direction of motion.