# Angular acceleration, tangential acceleration

katie beisel

## Homework Statement

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?

## Homework Equations

a = change in w/ change in t
tangential acceleration = ra

## The Attempt at a Solution

2pi/21.5 s = .292 rad/s = average w

Homework Helper
Gold Member
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?

katie beisel
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?
Δθ = ωit + 1/2αt^2

Homework Helper
Gold Member
Δθ = ωit + 1/2αt^2
Right. You can use it to get the angular acceleration.

katie beisel
Right. You can use it to get the angular acceleration.
but i don't know Δθ?

Homework Helper
Gold Member
but i don't know Δθ?
You do. The race ends after 1 round trip. That corresponds to how many radians?

katie beisel
You do. The race ends after 1 round trip. That corresponds to how many radians?
oh yeah 2pi rads = 0 + 1/2a(21.2 s)^2
i got a = .0272 rad/s^2