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Una rueda que gira a 300 r.P.M. Aumenta su velocidad bajo una aceleración angular de 6 2 s rad : calcula: a) La velocidad angular después de 10 s. b) El número de vueltas que da en ese tiempo. Respuestas: f = 873.0 r.P.M.  = 97.746 vueltas.

Sagot :

Answer:

a)   w = 873 rev,  b)  θ = 97.75 rev

Explanation:

This is a rotation kinematics exercise

         w = w₀ + α t

         θ = θ₀ + w₀ t + ½ α t²

let's start by reducing the magnitudes to the SI system

         w₀ = 300 rpm (2pi rad / 1 rev) (1 min / 60s) = 31.42 rad / s

          α = 6 rad / s²

a) let's look for the angular velocity

            w = 31.42 + 6 10

             w = 91.42 rad / s

b) θ₀ = 0

             θ = 0 + 31.42 to + ½ 6 10²

             θ = 614.2 rad

As they ask for the result in rpm and revolutions, let's carry out the reduction

         w = 91.42 rad / s (1 rev / 2pi rad) (60 s / 1min)

         w = 873 rev

         θ = 614.2 rad (1 rev / 2pi rad)

         θ = 97.75 rev

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