Hello, I was trying to do this problem and then I looked at the solution manual and found something that confused me. I am having trouble distinguishing between centripetal and radial acceleration. According to the equation in the book [tex]a_r=-a_c[/tex], which kind of confuses me. Isn't a centripetal acceleration vector pointed towards the center of a circle in uniform circular motion? Then why do they draw the radial acceleration vector, which has the opposite sign of the centripetal acceleration vector, pointing towards the center of the circle also? Aren't they supposed to be pointing in opposite directions? In the solution manual, he draws the radial acceleration vector, but then uses the centripetal equation for the solution. Can someone explain this to me? Particularly how centripetal and radial acceleration relate to one another. An analogy would nice if possible. Thx.(adsbygoogle = window.adsbygoogle || []).push({});

Here is a http://i218.photobucket.com/albums/cc304/JustSomeGuy805/PHYSCS.jpg" [Broken] of what I am talking about where the radial acceleration vector is drawn but then the centripetal acceleration equation is used instead.

1. The problem statement, all variables and given/known data

A train slows down as it rounds a sharp horizontal turn, slowing from 90.0 km/h to 50.0 km/h in the 15.0 seconds that it takes to round the bend. The radius of the curve is 150 m. Compute the acceleration at the moment the train speed reaches 50.0 km/h. Assume that it continues to slow down at this time at a constant rate.

2. Relevant equations

v=velocity, a=acceleration, r=radius

radial acceleration: [tex]{a_r} = - {{{v^2}} \over r}[/tex]

tangential acceleration: [tex]{a_t} = \left| {{{dv} \over {dt}}} \right|[/tex]

acceleration vector: [tex]\vec a = {{\vec a}_r} + {{\vec a}_t}[/tex]

centripetal acceleration: [tex]{a_c} = {{{v^2}} \over r}[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Confused about Centripetal and Radial Acceleration

**Physics Forums | Science Articles, Homework Help, Discussion**