# Angular acceleration, tangential acceleration

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1. Feb 20, 2016

### katie beisel

1. The problem statement, all variables and given/known data
Two go-karts race around a course that has concentric circular tracks. The radius of the inner track is 15.0 m, and the radius of the outer track is 19.0 m. The go-karts start from rest at the same angular position and time, and move at the same constant angular acceleration. The race ends in a tie after one complete lap, which takes 21.5 seconds. (a) What is the common angular acceleration of the carts? (b) What is the tangential acceleration of the inner cart? (c) What is the tangential acceleration of the outer cart?

2. Relevant equations
a = change in w/ change in t
tangential acceleration = ra

3. The attempt at a solution
2pi/21.5 s = .292 rad/s = average w

2. Feb 21, 2016

### cnh1995

You need to use the kinematical equations for angular motion. What is the equation relating angular displacement θ, angular velocity ω, angular acceleration α and time t?

3. Feb 21, 2016

### katie beisel

Δθ = ωit + 1/2αt^2

4. Feb 21, 2016

### cnh1995

Right. You can use it to get the angular acceleration.

5. Feb 21, 2016

### katie beisel

but i dont know Δθ?

6. Feb 21, 2016

### cnh1995

You do. The race ends after 1 round trip. That corresponds to how many radians?

7. Feb 21, 2016

### katie beisel

oh yeah 2pi rads = 0 + 1/2a(21.2 s)^2
i got a = .0272 rad/s^2