# Rotational motion and tangential speed?

1. Dec 13, 2009

### yramos9

1. The problem statement, all variables and given/known data
A 919 kg rollercoaster is about to go up a hill that acts as the top of a circle 16.21m in diameter. What is the fastest that car can move (in m/s) without leaving a track?
known:
mass: 919 kg
diameter: 16.21

2. Relevant equations
Vt=r$$\omega$$
$$\omega$$=$$\theta$$/time

3. The attempt at a solution
i have no idea how to work this out with out knowing the time or speed or somekind of time measurement. Is there another way to solve this?

2. Dec 13, 2009

### Pythagorean

centrifugal force

force balance

free body diagram

3. Dec 13, 2009

### yramos9

huh??

4. Dec 13, 2009

### Pythagorean

Draw a free-body diagram of the cart with centrifugal force pulling it up and gravity pulling it down. The sum of the forces on the cart should be zero in the radial direction (since that's the direction for which you don't want motion). Centrifugal force should be a function of tangential velocity, which is the velocity in question.

What level of physics is this? Gravity would realistically be a function of the angle about the center of the circle and only be exactly g when the cart is exactly on the tip of the half-circle. But you could probably neglect this if it's an introductory physics course.

5. Dec 13, 2009

### yramos9

this is 11th grage physics pre-ap.. i dont think ive learned what youre trying to teach me.

6. Dec 13, 2009

### ideasrule

When gravity can provide the centripetal acceleration required to keep the roller coaster on the track, the coaster doesn't fly off. Otherwise, it does. When does gravity exactly equal the required centripetal force? (Hint: F=ma)