Tangential and radial particle acceleration

In summary, the student was trying to solve for the y-coordinate of a particle that was moving in a circle and was given the radial acceleration in terms of magnitude and direction. They plugged in the values for the radial acceleration and got an incorrect answer. Then, they tried plugging in the value for the centripetal acceleration and got an incorrect answer as well. If they had used the y-coordinate as given, they would have gotten an incorrect answer for the x coordinate as well.
  • #1
Why-not2007
3
0

Homework Statement


A particle moves in the xy plane in a circle centered origin. At a certain instant the velocity and acceleration of the particle are 4.6j m/s and (2.3i - 2.1j) m/s^2. What are the x and y coordinates of the particle at this moment


Homework Equations


ar=-v^2/r


The Attempt at a Solution


I took the magnitude of the radial acceleration and got 3.11 m/s^2 and plugged it into the equation. I got -6.8 for my radius and was told that was the wrong answer for the x coordinate. Then I tried plugging in 2.3 for the radial acceleration and got -9.2 for my radius. Does the -2.1j m/s^2 not play a factor in this problem? I got x=-9.2, but I don't know how to solve for the y component of the problem.
 
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  • #2
Why-not2007 said:
I took the magnitude of the radial acceleration and got 3.11 m/s^2 and plugged it into the equation.
How did you get this? Are you assuming that the particle is moving with a constant speed? (You are given the total acceleration, not the radial acceleration.)
I got -6.8 for my radius and was told that was the wrong answer for the x coordinate. Then I tried plugging in 2.3 for the radial acceleration and got -9.2 for my radius. Does the -2.1j m/s^2 not play a factor in this problem? I got x=-9.2, but I don't know how to solve for the y component of the problem.
The velocity should tell you the y-coordinate, since it moves in a circle.
 
  • #3
Why-not2007 said:

Homework Statement


A particle moves in the xy plane in a circle centered origin. At a certain instant the velocity and acceleration of the particle are 4.6j m/s and (2.3i - 2.1j) m/s^2. What are the x and y coordinates of the particle at this moment


Homework Equations


ar=-v^2/r


The Attempt at a Solution


I took the magnitude of the radial acceleration and got 3.11 m/s^2 and plugged it into the equation. I got -6.8 for my radius and was told that was the wrong answer for the x coordinate. Then I tried plugging in 2.3 for the radial acceleration and got -9.2 for my radius. Does the -2.1j m/s^2 not play a factor in this problem? I got x=-9.2, but I don't know how to solve for the y component of the problem.
The velocity is given as being in the 'j' direction only. That should give you a hint on the possible location of the y coordinate. Your value of the centripetal acceleration that you must use depends on the value of the y coordinate you must find first.
 
  • #4
The y coordinate equal 0?
 
  • #5
Why-not2007 said:
The y coordinate equal 0?
Absolutely. That's the only way to make sense of the given velocity, since that velocity must be tangential to the circle at all times.
 
  • #6
Thanks, I appreciate the help.
 

What is tangential particle acceleration?

Tangential particle acceleration refers to the change in velocity of a particle along its path of motion, in the direction of the tangential component of its velocity vector.

What is radial particle acceleration?

Radial particle acceleration refers to the change in direction of a particle's motion, caused by a force acting towards or away from a central point.

What is the difference between tangential and radial particle acceleration?

The main difference between tangential and radial particle acceleration is the direction of the acceleration. Tangential acceleration acts in the direction of motion, while radial acceleration acts perpendicular to the direction of motion.

What factors affect tangential and radial particle acceleration?

The factors that affect tangential and radial particle acceleration include the magnitude and direction of the force acting on the particle, the mass of the particle, and the initial velocity of the particle.

How are tangential and radial particle acceleration related to circular motion?

Tangential acceleration is responsible for changing the speed of a particle in circular motion, while radial acceleration causes the particle to change direction and stay on a circular path. Both types of acceleration are essential for maintaining circular motion.

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