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/
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