Acceleration of a curved trajectory

In summary, Feynman discusses the tangent acceleration and its relation to changes in speed and velocity in Chapter 11 of his Lectures on Physics, Volume 1. He also mentions the idea of neglecting certain factors, such as those that go to 0 quicker than the relevant effect, when considering acceleration. There is also a question regarding the magnitude of velocity and how it can be multiplied with an angle.
  • #1
Fyreth
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Feynman_Lectures_on_Physics_Volume_1_Chapter_11

In paragraph 11-6 he says that the tangent acceleration is the change of speed v but if I look at fig. 11-8 the change in speed is slightly smaller than the change in tangent velocity. (I drew a circle with the radius of the speed of v_I that has it's middle in the origin of the vectors mentally.) I assume he just neglects that difference but I don't really understand the idea of neglecting certain things. What things can you neglect and what not?
He also says that the acceleration at right angles to the curve is the magnitude of the velocity times the change in angle. The magnitude of which velocity? v_I or v_II? How can you just multiply speed with an angle? I know you can if you use sine, cosine or something like that but multiply it with an angle directly?
 
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  • #2
You can neglect things which go to 0 quicker than your relevant effect, if the time-step goes to 0. In other words, everything where effectsize/timestep goes to 0 as timestep goes to 0.

In general, your post looks confusing to me, therefore the very general answer.
 

1. What is acceleration of a curved trajectory?

Acceleration of a curved trajectory is the rate of change of velocity of an object moving along a curved path. It is a vector quantity, meaning it has both magnitude and direction.

2. How is acceleration of a curved trajectory calculated?

To calculate acceleration of a curved trajectory, you need to know the object's initial and final velocities, as well as the time it takes for the object 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 is the difference between acceleration of a curved trajectory and linear acceleration?

The main difference is that acceleration of a curved trajectory takes into account changes in direction, while linear acceleration only measures changes in speed along a straight line. Acceleration of a curved trajectory is also a more complex calculation, as it involves vector components.

4. Can acceleration of a curved trajectory be negative?

Yes, acceleration of a curved trajectory can be negative. This means that the object is slowing down or changing direction in the opposite direction of its initial motion.

5. How does acceleration of a curved trajectory affect an object's path?

Acceleration of a curved trajectory will cause an object to deviate from its initial path and follow a curved trajectory. The direction of acceleration will determine the direction of the curvature, while the magnitude of acceleration will determine the tightness of the curve.

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