# Newton's 2nd law in circular motion

## Homework Statement

Daytona International Speedway in Florida. Both of its courses feature four story, 31.0 degree banked curves with max radius of 316 if a car negotiates the curve too slowly it tends to slip down the incline of the turn whearas if it going too fast it may begin to slide up the incline. find the centripetal acceleration on the curve so won't slip up or down and calculate the speed (neglect friction

F=ma
v^2/r

## The Attempt at a Solution

I have the solution it is 5.89 m/s^2 and 43.1 m/s, but i don't understand why the normal force uses cos. It says use the y-component of Newton's second law to solve for the normal force n....so why am I supposed to use cos instead of sin and how can I know for future problems that are similar?

ma= F = n + mg
ncostheta -mg = 0
n= mg/ costheta
F = mg tan theta
centripetal acceleration = g*tan*theta

then v^2/r = 43.1

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I am having trouble understanding why cos is the y-component of New's second law in regards to solving for the normal force of a problem regarding circular motion (car on a banked racetrack) and in linear motion the y-component of Newton's second law was sin. How do I know whether the y component pertains to cos or sin for a circular problem or if it is always cos then why?!?!

cristo
Staff Emeritus
You have to look at which angle you have labelled. Do you have a specific question?

cristo
Staff Emeritus