Acceleration around a Corner

Date: 09/17/2005 at 00:05:04
From: Justin
Subject: Acceleration around a corner

What is the formula to find out the acceleration of an object going 
around a corner?

Our teacher has told us to research the formula of the acceleration 
of an object around a corner.  I have been thinking about different 
ways it could be solved, but the things I have tried are not working.

I think what you have to do is to first get the velocity, then 
somehow figure the degrees of the corner and multiply them.  Then, 
you divide that by the distance.  Would that work?

Date: 09/17/2005 at 10:39:23
From: Doctor Jerry
Subject: Re: Acceleration around a corner.

Hello Justin,

I'd suggest that you imagine an object going around a corner on part
of a circle.

When you do that, you can think about the "angular velocity" of the
object, which is the change in the angular position of the object per
time unit.  It's best to use radians, not degrees, in measuring the
angle.  A circle has 360 degrees all the way around; in radians that
is 2*pi radians (where pi=3.141592654...).  So, to convert from
degrees to radians, just multiply the degrees times 2*pi/360 (or
pi/180, same thing).  

A car might go around a circular curve so that, measured from the
center of the circle, in one second it moves through an angle of 10
degrees or, better, 10*pi/180 = pi/18 radians.  Its angular velocity 
is pi/18 radians per second.  pi/18 ~ 0.17

If you know the angular velocity of the car at many times during the
time it is going around the curve, you can find the angular
acceleration at a given time.

For example, if you know these times t and angular velocities w

  (t,w) = (0,0.10), (0.5,0.12), (1.0,0.14), (1.5,0.17), (2.0,0.20)

you can figure out the angular acceleration at, say, t = 1.0.  The
angular acceleration is how much the angular velocity changes in 1 second.

Can you approximate the angular acceleration at t = 1.0 ?


- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/