# Acceleration for a curved trajectory

• Jazzyrohan

#### Jazzyrohan

In feynman lectures on physics volume 1
Excerpt 11-6
I don't get how the equation \begin{equation*} \Delta v_\perp=v\,\Delta\theta \end{equation*} is found.

Me neither, I don't have a copy of the Feynman lectures and don't have a clou what this all means.

haushofer said:
Me neither, I don't have a copy of the Feynman lectures and don't have a clou what this all means.
They are available online.

It would be helpful to link, at least to section 11-6 even if you can't link to the equation: http://www.feynmanlectures.caltech.edu/I_11.html#Ch11-S6

##\sin\Delta\theta\simeq\Delta\theta## if ##\Delta\theta<<1##, is the relevant fact, I think. Then the result follows from figure 11-8.

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## 1. What is acceleration for a curved trajectory?

Acceleration for a curved trajectory is the rate of change of velocity for an object moving along a curved path. It measures how quickly an object's velocity changes in terms of both magnitude and direction.

## 2. How is acceleration for a curved trajectory calculated?

To calculate acceleration for a curved trajectory, you need to know the initial and final velocities of the object, as well as the time it takes to travel between those two points. The formula for acceleration is: a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

## 3. What factors affect acceleration for a curved trajectory?

The main factors that affect acceleration for a curved trajectory are the object's mass, the force acting on the object, and the curvature of the path it is traveling on. In general, the greater the mass of the object, the more force is needed to accelerate it. A greater force will also result in a larger acceleration. Additionally, a tighter curve will require a higher acceleration compared to a more gradual curve.

## 4. How does acceleration for a curved trajectory differ from linear acceleration?

Acceleration for a curved trajectory is different from linear acceleration because it takes into account changes in both speed and direction. Linear acceleration only measures the change in speed, while acceleration for a curved trajectory also considers changes in direction. This is due to the fact that an object moving along a curved path is constantly changing its direction of motion.

## 5. What are some real-world examples of acceleration for a curved trajectory?

Some real-world examples of acceleration for a curved trajectory include the motion of a car going around a sharp turn, the movement of a rollercoaster along its track, and the flight path of a rocket as it launches into space. Any object moving along a curved path, such as a ball being thrown or a bird flying in a circle, also experiences acceleration for a curved trajectory.