Rotational dynamics of two cars

1. Nov 12, 2008

zoner7

1. The problem statement, all variables and given/known data
Two cars race around a circular track. Car A accelerates at 0.340 rad/s2 around the track, and car B at 0.270 rad/s2. They start at the same place on the track and car A lets the slower-to-accelerate car B start first. Car B starts at time t = 0. When car A starts, car B has an angular velocity of 1.40 rad/s. At what time does car A catch up to car B?

3. The attempt at a solution

So first I calculated the time that car B accelerates before car A begins to move using acceleration of car B and its final angular velocity.

My time value is 5.185

Then I calculated the distance that car B travels until it attains an angular velocity of 1.4.

My distance is 3.629.

Then I used the linear motion equations to set the final distances of cars A and B to one another, resulting in the following equation after simplified:

1/2 Alpha(car A) t^2 - 1/2 Alpha(car B) t^2 - Omega (initial car B) t - Theta (car B).

After plugging in values, I used the quadratic equation and found a time value of 42.44 seconds.

I added the time that Car B travels before it reaches car A: 5.185 + 42.44 and found an ultimate time of 47.625.

But if I plug each the smaller time into car A's linear motion equation and the larger into Car B's, the distances are unequal...

help...?

Thank you in advance.

2. Nov 12, 2008

LowlyPion

When you plug the longer time into the slower cars equation it's changed. The proper equation for that car then has no initial conditions.

X = 1/2*.27*(47.625)2 = 1/*.34*(42.44)2