Acceleration of a particle moving around a circular path.

[necromanzer52]

Homework Statement

A particle moves along a circular path of radius 6 m, with constant linear acceleration of 1 m/s/s. Determine its total acceleration after 2 seconds.

Homework Equations

Can't find any. That's why I'm here.

The Attempt at a Solution

I assume there's some equation I can just plug numbers into to calculate the acceleration due to the fact it's moving in a circle, then use pythagoras to get the magnitude, but I can't find any. Either that or it's a trick question and the answer is always 1 m/s/s.

 

[rude man]

No trick question.

The safe thing is to dig up your expression for acceleration in cylindrical coordinates. However, it can also be done by realizing there are two accelerations involved and they add vectorially. Assume the motion is in the direction of increasing ψ.

 

[necromanzer52]

Oh. It's that big long one with the four components, isn't it? And I integrate to get expressions for velocity & position.

What is ψ?

 

[rude man]

Oh. It's that big long one with the four components, isn't it? And I integrate to get expressions for velocity & position.

What is ψ?

Yes, the total expression for the acceleration vector in 3 dimensions has (of course) 3 components, of 2 terms each.

ψ is the angle part of the cylindrical coordinte system. The PF 'quick symbol' table doesn't have a phi, unfortunately. Maybe should have used θ instead.

Why do you want to integrate to get v and s? The problem doesn't ask for them ...

 

[Redbelly98]

Homework Statement

A particle moves along a circular path of radius 6 m, with constant linear acceleration of 1 m/s/s. Determine its total acceleration after 2 seconds.

Homework Equations

Can't find any. That's why I'm here.

The Attempt at a Solution

I assume there's some equation I can just plug numbers into to calculate the acceleration due to the fact it's moving in a circle, then use pythagoras to get the magnitude, but I can't find any. Either that or it's a trick question and the answer is always 1 m/s/s.

This appears to be either a high school physics or a college freshman physics problem. If so, then by "total acceleration" I presume they mean centripetal and tangential components of acceleration. Check your physics textbook for the discussion of centripetal or circular motion (not to be confused with rotational motion, that is different). The relevant equation for centripetal acceleration should be there.

Also, why is this (apparently) introductory physics problem being posted in the engineering homework area? Can you clarify what course subject this assignment is for?

Final note: this problem cannot be solved without knowing the initial speed of the particle. Did you by any chance omit some information? Does the phrase "starts from rest" happen to appear in the problem statement somewhere?

No trick question.

The safe thing is to dig up your expression for acceleration in cylindrical coordinates. However, it can also be done by realizing there are two accelerations involved and they add vectorially. Assume the motion is in the direction of increasing ψ.

If this is an introductory physics problem as I strongly suspect, then bringing in cylindrical coordinates is an unnecessary complication.

 

[rude man]

If this is an introductory physics problem as I strongly suspect, then bringing in cylindrical coordinates is an unnecessary complication.

It's a lot more complicated if you don't!

 

[necromanzer52]

I posted it here as I'm a college freshman in engineering. And as this is a classical mechanics question it seems like the right board.

Anyway, I don't have a textbook and I can't find the relevant equation on the internet.

Also it says it starts to move, so I take that to mean it started from rest.

 

[rude man]

I defer to Mr. Redbelly on this.

 

[Redbelly98]

I posted it here as I'm a college freshman in engineering. And as this is a classical mechanics question it seems like the right board.

Anyway, I don't have a textbook and I can't find the relevant equation on the internet.

Also it says it starts to move, so I take that to mean it started from rest.

Your situation sounds rather unusual: an engineering student who has not taken introductory physics yet.

Be that as it may, below are a couple of online references for acceleration of particles that move in a circle. But first, some important things to keep in mind are:

1. The velocity (a vector) always points in the direction tangent to the circle, no matter where the particle is on the circle. We call this the tangential direction.
2. The acceleration (also a vector) can have one or two components. It always has a component toward the center of the circular path (the centripetal acceleration), which causes the particle to curve to the left or right. And it may or may not have a tangential component (in the direction of the velocity) -- it does if the particle is speeding up or slowing down, as in your problem. If the speed were constant, then the tangential acceleration would be zero.

You can find out more of the basics here:
http://en.wikipedia.org/wiki/Acceleration#Tangential_and_centripetal_acceleration
http://theory.uwinnipeg.ca/physics/circ/node6.html

Hope that helps. Once you understand better what's going on, solving this problem pretty much begins with figuring out the speed of the particle (that starts from rest ) after 2 seconds.