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3 years ago

7

A solid disk of radius 1.4 cm and mass 430 g is attached by a wire to one of its circular faces. It is twisted through an angle

of 10 o and released. If the spring has a torsion constant of 370 N-m/rad, what is the frequency of the motion

1 answer:

Neporo4naja [7]3 years ago

5 0

Answer:

f= 4,186 10² Hz

Explanation:

El sistema descrito es un pendulo de torsión que oscila con con velocidad angular, que esta dada por

w = √ k/I

donde ka es constante de torsion de hilo e I es el momento de inercia del disco

El momento de inercia de indican que giran un eje que pasa por enronqueces

I= ½ M R2

reduzcamos las cantidades al sistema SI

R= 1,4 cm = 0,014 m

M= 430 g = 0,430 kg

substituimos

w= √ (2 k/M R2)

calculemos

w = RA ( 2 370 / (0,430 0,014 2)

w = 2,963 103 rad/s

la velocidad angular esta relacionada con la frecuencia por

w =2pi f

f= w/2π

f= 2,963 10³/ (2π)

f= 4,186 10² Hz

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