# Non-Uniform Circular Motion Problem

1. Sep 15, 2009

### creechur

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

A car starts from rest on a curve with radius 150m, with an acceleration of 1.8 m/s2. How many revolutions will the car make before the magnitude of its acceleration is 2.40 m/s2?

2. Relevant equations

at2 + ar2 = total acceleration2

theta = omega (t) + .5 (acceleration) (t)2

3. The attempt at a solution

I solved for velocity by plugging in v2/ R into the acceleration triangle equation. Then I solved for "t" by dividing my velocity by the acceleration and got 15 m/s for velocity and 8.3 seconds for time. I plugged that into the position equation and got 62.5 radians, divided by 2pi and got 9.95 revolutions. That was wrong - tips please?

Last edited: Sep 15, 2009
2. Sep 15, 2009

### Hootenanny

Staff Emeritus
This equation is incorrect,
If we look at the dimensions we find that,

[θ] = 1 (i.e. dimensionless)
[ωt] = T-1T = 1 (i.e. dimensionless)
[at2] = LT-2T2 = L (i.e. a length)

Do you know any rotational kinematic equation? (They are analogous to the linear kinematic equations).

3. Sep 15, 2009

### Fightfish

I presume he meant angular acceleration, $$\alpha$$ by "acceleration" in the equation though?
The problem with using that equation is that the angular acceleration of the car is not constant, depending on the velocity of the car at any given time.

4. Sep 15, 2009

### Hootenanny

Staff Emeritus
Perhaps the OP did mean angular acceleration. However, a constant tangential acceleration implies that the angular acceleration is also constant, since the two are directly proportional.

5. Sep 15, 2009

### Fightfish

Oh right, must have confused angular acceleration and centripetal acceleration for a moment there :(
That's probably what creechur must've done too.

I don't think I would bother with rotational kinematics for this question though, the relation arc length travelled s = vt, where v is the tangential velocity along with translational kinematics should suffice.

Last edited: Sep 15, 2009
6. Sep 15, 2009

### creechur

I did mean angular acceleration by the "a" in my equation, I just don't know how to make the symbols. If the approach I have taken isn't correct, what else would you do?

7. Sep 15, 2009

### Fightfish

Consider the linear distance travelled by the car during the period. In one revolution, the car would have transversed a distance of $$2 \pi r$$. Thus, the number of revolutions can be obtained.

8. Sep 15, 2009

### creechur

How do you take into account the change in acceleration?

9. Sep 15, 2009

### Fightfish

From the question, it is implied that tangential acceleration does not change; it is the centripetal or radial acceleration that increases as the car speeds up. Didn't you assume that when you solved for the final velocity as well?