Solving an Exercise Involving Particle P Moving Along the X-Axis

In summary, the conversation is about a particle moving with constant speed along the X axis of a reference system and finding its movement in another system with the same origin but rotating in a clockwise direction. The individual asks if their solution is correct and if they need to find acceleration. They are then advised to differentiate again and consider Coriolis and centrifugal acceleration.
  • #1
PhoenixWright
20
1
Hello.

I have the following exercise, and I would like you to say to me if I have it right and how to proceed:

"A particle P moves with constant speed v along the X axis of a reference system O, being x0 = 0 the position in t = 0. Describe the movement on another system O' with the same origin of coordinates and rotating with angular velocity constant ω in the sense clockwise."

H56wp4r.png


I have tried to solve as follows:
54J53Vp.png


So far, is my point correct?

Now, I had thought find the acceleration:

CmvBXqb.png

Is it correct?

Thank you!
 
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  • #2
up :frown:
 
  • #3
Why don't you just differentiate again?
But I'm not sure what the question is asking for. Isn't your expression for r' an adequate description? Do you need to find the velocity and acceleration vectors?
 
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Likes PhoenixWright
  • #4
haruspex said:
Why don't you just differentiate again?
But I'm not sure what the question is asking for. Isn't your expression for r' an adequate description? Do you need to find the velocity and acceleration vectors?

Thank you!

Eventually I realized I could differentiate again. I believed that in this case I need to apply Coriolis and centrifugal acceleration, but I was reading and saw that could also solve in this way a moment ago.
 

1. How do I determine the position of Particle P at a specific time t?

To determine the position of Particle P at a specific time t, you will need to use the formula x = x0 + v0t + 1/2at2, where x0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is the time. Plug in the values given in the problem to solve for x.

2. What is the difference between displacement and distance?

Displacement is the straight line distance between the initial and final position of Particle P, while distance is the total length traveled by Particle P along the x-axis. Displacement takes into account the direction of motion, while distance does not.

3. How do I calculate the velocity of Particle P?

The velocity of Particle P can be calculated using the formula v = v0 + at, where v0 is the initial velocity, a is the acceleration, and t is the time. Plug in the values given in the problem to solve for v.

4. What is the acceleration of Particle P?

The acceleration of Particle P can be calculated using the formula a = (v - v0) / t, where v is the final velocity, v0 is the initial velocity, and t is the time. If the problem does not provide values for v, v0, and t, you can also use the formula a = F / m, where F is the net force acting on Particle P and m is its mass.

5. How do I know if Particle P is accelerating or moving at a constant velocity?

If the acceleration of Particle P is equal to zero, then it is moving at a constant velocity. If the acceleration is not equal to zero, then Particle P is accelerating. You can also determine this by looking at the velocity graph of Particle P. A straight, horizontal line indicates constant velocity, while a sloping line indicates acceleration or deceleration.

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