UCSal (Adapt.) Duas partículas descrevem órbitas circulares concêntricas com velocidades angulares constantes de 3ω e 2ω, respectivamente, no mesmo...

Para que as duas partículas voltem a passar juntas pelo mesmo raio de referência r0, é necessário que a diferença angular entre elas seja um múltiplo inteiro de 2π. A diferença angular inicial é de 3ω - 2ω = ω. Portanto, o menor intervalo de tempo para que elas voltem a passar juntas pelo mesmo raio de referência r0 é dado por: Δt = 2π/ω Substituindo as velocidades angulares dadas, temos: Δt = 2π/ω = 2π/(3ω - 2ω) = 2π/ω = 2π/ω = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π/(ω) = 2π