A torsional pendulum consists of a 5 kg uniform disk with a diameter of 50 cm attached at its center to a rod 1.5 m in length. The torsional spring constant is 0.625 N-m/rad. Disregarding the mass of the rod, what is the natural frequency of the torsional pendulum?

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DeniceSandidge DeniceSandidge · Answer 1 · 2020-02-25T11:29:52+01:00

Answer:

natural frequency of the torsional pendulum = 1.4 rad/s

Explanation:

given data

mass = 5 kg

diameter = 50 cm = 0.50 m

so radius R = 0.25 m

length = 1.5 m

torsional spring constant = 0.625 N-m/rad

solution

first we get here moment of inertia that is

moment of inertia = mR² .........1

moment of inertia = 5 × 0.25²

moment of inertia = 0.3125 kg-m²

so now we get here natural frequency of the torsional pendulum that is

natural frequency of the torsional pendulum = [tex]\sqrt{\frac{Kt}{I} }[/tex] ..................2

here Kt is torsional spring constant and I is moment of inertia

natural frequency of the torsional pendulum = [tex]\sqrt{\frac{0.625}{3125} }[/tex]

natural frequency of the torsional pendulum = 1.4 rad/s