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Los datos que tienes son:
Ф = 456 rev
t = 34 s
ω = ?
Convertimos las unidades al SI
1 rev-------------------------2πrad
456 rev----------------------x
x = (456 rev * 2πrad)/ 1 rev
x = (456 * 2πrad) / 1
x = 912πrad / 1
x = 912 (3,1416) rad / 1
x = 2865,14 rad / 1
x = 2865,14 rad
Calculamos la velocidad angular
ω = Ф/t
ω = 2865,14 rad / 34 s
ω = 84,27 rad/s------------------Respuesta